Results of Mathieu Functions and Hill’s Equation
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| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 28.1#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{Se}_{n}(s,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}} | S*exp(1)[n]*(s , z)=(MathieuCE(n, q, z))/(MathieuCE(n, q, 0)) |
S*Subscript[E*, n]*(s , z)=Divide[MathieuC[n, q, z],MathieuC[n, q, 0]] |
Failure | Failure | Error | Error |
| 28.1#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{So}_{n}(s,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}} | S*o[n]*(s , z)=(MathieuSE(n, q, z))/(subs( temp=0, diff( MathieuSE(n, q, temp), temp$(1) ) )) |
S*Subscript[o, n]*(s , z)=Divide[MathieuS[n, q, z],D[MathieuS[n, q, temp], {temp, 1}]/.temp-> 0] |
Failure | Failure | Skip | Error |
| 28.1#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{Se}_{n}(c,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}} | S*exp(1)[n]*(c , z)=(MathieuCE(n, q, z))/(MathieuCE(n, q, 0)) |
S*Subscript[E*, n]*(c , z)=Divide[MathieuC[n, q, z],MathieuC[n, q, 0]] |
Failure | Failure | Error | Error |
| 28.1#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{So}_{n}(c,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}} | S*o[n]*(c , z)=(MathieuSE(n, q, z))/(subs( temp=0, diff( MathieuSE(n, q, temp), temp$(1) ) )) |
S*Subscript[o, n]*(c , z)=Divide[MathieuS[n, q, z],D[MathieuS[n, q, temp], {temp, 1}]/.temp-> 0] |
Failure | Failure | Skip | Error |
| 28.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+\pi) = e^{\pi\iunit\nu}w(z)} | w*(z + Pi)= exp(Pi*I*nu)*w*(z) |
w*(z + Pi)= Exp[Pi*I*\[Nu]]*w*(z) |
Failure | Failure | Fail 4.397533327+8.455409696*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}8.455409696+4.488232549*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}4.488232549+.4303561791*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.4303561791+4.397533327*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[4.397533326856219, 8.455409698756243] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-323.35991533293776, 98.99067506580616] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[332.24568120925454, 98.99067506580616] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.4882325494605135, 8.455409698756243] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)} | w*(z + Pi)+ w*(z - Pi)= 2*cos(Pi*nu)*w*(z) |
w*(z + Pi)+ w*(z - Pi)= 2*Cos[Pi*\[Nu]]*w*(z) |
Failure | Failure | Fail 327.7574484+98.56031892*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}98.56031892-327.7574484*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-327.7574484-98.56031892*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-98.56031892+327.7574484*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[327.757448659794, 98.56031888824567] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-327.757448659794, 98.56031888824567] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[327.757448659794, 98.56031888824567] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-327.757448659794, 98.56031888824567] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}} | w*(z)= sum(c[2*n]*exp(I*(nu + 2*n)* z), n = - infinity..infinity) |
w*(z)= Sum[Subscript[c, 2*n]*Exp[I*(\[Nu]+ 2*n)* z], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 28.2.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0,&a = \Mathieueigvala{2n}@{q},\\ w_{\mbox{\tiny I}}(\tfrac{1}{2}\pi;a,q)} | 0 , |
0 , |
Error | Error | - | - |
| 28.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0,&a = \Mathieueigvalb{2n+1}@{q},\\ w_{\mbox{\tiny II}}(\tfrac{1}{2}\pi;a,q)} | 0 , |
0 , |
Error | Error | - | - |
| 28.2.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{n}@{0} = n^{2}} | MathieuA(n, 0)= (n)^(2) |
MathieuCharacteristicA[n, 0]= (n)^(2) |
Successful | Successful | - | - |
| 28.2.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvalb{n}@{0} = n^{2}} | MathieuB(n, 0)= (n)^(2) |
MathieuCharacteristicB[n, 0]= (n)^(2) |
Successful | Successful | - | - |
| 28.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvalb{1}@@{q} < \Mathieueigvala{1}@@{q}} | MathieuB(1, q)< MathieuA(1, q) |
MathieuCharacteristicB[1, q]< MathieuCharacteristicA[1, q] |
Failure | Failure | Successful | Successful |
| 28.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{1}@@{q} < \Mathieueigvalb{2}@@{q}} | MathieuA(1, q)< MathieuB(2, q) |
MathieuCharacteristicA[1, q]< MathieuCharacteristicB[2, q] |
Failure | Failure | Skip | Successful |
| 28.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvalb{2}@@{q} < \Mathieueigvala{2}@@{q}} | MathieuB(2, q)< MathieuA(2, q) |
MathieuCharacteristicB[2, q]< MathieuCharacteristicA[2, q] |
Failure | Failure | Skip | Successful |
| 28.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{2}@@{q} < \Mathieueigvalb{3}@@{q}} | MathieuA(2, q)< MathieuB(3, q) |
MathieuCharacteristicA[2, q]< MathieuCharacteristicB[3, q] |
Failure | Failure | Skip | Successful |
| 28.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{1}@@{q} < \Mathieueigvalb{1}@@{q}} | MathieuA(1, q)< MathieuB(1, q) |
MathieuCharacteristicA[1, q]< MathieuCharacteristicB[1, q] |
Failure | Failure | Skip | Successful |
| 28.2.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}} | MathieuA(2*n, - q)= MathieuA(2*n, q) |
MathieuCharacteristicA[2*n, - q]= MathieuCharacteristicA[2*n, q] |
Failure | Failure | Successful | Successful |
| 28.2.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}} | MathieuA(2*n + 1, - q)= MathieuB(2*n + 1, q) |
MathieuCharacteristicA[2*n + 1, - q]= MathieuCharacteristicB[2*n + 1, q] |
Failure | Failure | Successful | Successful |
| 28.2.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}} | MathieuB(2*n + 2, - q)= MathieuB(2*n + 2, q) |
MathieuCharacteristicB[2*n + 2, - q]= MathieuCharacteristicB[2*n + 2, q] |
Failure | Failure | Successful | Successful |
| 28.2#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{0}@{z}{0} = 1/\sqrt{2}} | MathieuCE(0, 0, z)= 1/sqrt(2) |
MathieuC[0, 0, z]= 1/Sqrt[2] |
Failure | Successful | - | - |
| 28.2#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{n}@{z}{0} = \cos@{nz}} | MathieuCE(n, 0, z)= cos(n*z) |
MathieuC[n, 0, z]= Cos[n*z] |
Successful | Failure | - | Fail
Complex[6.510464566583027, -0.7008927266021505] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.262006072549275, -34.68845328285399] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.510464566583027, 0.7008927266021505] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[11.262006072549275, 34.68845328285399] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{n}@{z}{0} = \sin@{nz}} | MathieuSE(n, 0, z)= sin(n*z) |
MathieuS[n, 0, z]= Sin[n*z] |
Successful | Failure | - | Fail
Complex[0.8057439410809155, 6.510552888635757] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[34.75636341426024, 11.321973340262975] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8057439410809155, -6.510552888635757] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[34.75636341426024, -11.321973340262975] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi} | int((MathieuCE(n, q, x))^(2), x = 0..2*Pi)= Pi |
Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}]= Pi |
Failure | Failure | Skip | Fail
Complex[-1.727379091216698, 1.4142135623730951] <- {Rule[Integrate[Power[MathieuC[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.727379091216698, -1.4142135623730951] <- {Rule[Integrate[Power[MathieuC[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, -1.4142135623730951] <- {Rule[Integrate[Power[MathieuC[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, 1.4142135623730951] <- {Rule[Integrate[Power[MathieuC[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 28.2#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi} | int((MathieuSE(n, q, x))^(2), x = 0..2*Pi)= Pi |
Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}]= Pi |
Failure | Failure | Skip | Fail
Complex[-1.727379091216698, 1.4142135623730951] <- {Rule[Integrate[Power[MathieuS[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.727379091216698, -1.4142135623730951] <- {Rule[Integrate[Power[MathieuS[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, -1.4142135623730951] <- {Rule[Integrate[Power[MathieuS[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.555806215962888, 1.4142135623730951] <- {Rule[Integrate[Power[MathieuS[n, q, x], 2], {x, 0, Times[2, Pi]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 28.2.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0} | int(MathieuCE(m, q, x)*MathieuCE(n, q, x), x = 0..2*Pi)= 0 |
Integrate[MathieuC[m, q, x]*MathieuC[n, q, x], {x, 0, 2*Pi}]= 0 |
Failure | Failure | Skip | Successful |
| 28.2.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0} | int(MathieuSE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi)= 0 |
Integrate[MathieuS[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}]= 0 |
Failure | Failure | Skip | Successful |
| 28.2.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0} | int(MathieuCE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi)= 0 |
Integrate[MathieuC[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}]= 0 |
Failure | Failure | Skip | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Integrate[Times[MathieuC[m, q, x], MathieuS[n, q, x]], {x, 0, Times[2, Pi]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Integrate[Times[MathieuC[m, q, x], MathieuS[n, q, x]], {x, 0, Times[2, Pi]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Integrate[Times[MathieuC[m, q, x], MathieuS[n, q, x]], {x, 0, Times[2, Pi]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Integrate[Times[MathieuC[m, q, x], MathieuS[n, q, x]], {x, 0, Times[2, Pi]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 28.2.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}} | MathieuCE(2*n, - q, z)=(- 1)^(n)* MathieuCE(2*n, q, (1)/(2)*Pi - z) |
MathieuC[2*n, - q, z]=(- 1)^(n)* MathieuC[2*n, q, Divide[1,2]*Pi - z] |
Failure | Failure | Successful | Fail
Complex[-35.48938782449842, 4.362541390270897] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.113008541051663, 1.5552980263308331] <- {Rule[n, 2], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[35.468444164343595, -60.307504750945526] <- {Rule[n, 3], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.4218686670701555, 4.355505323618388] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}} | MathieuCE(2*n + 1, - q, z)=(- 1)^(n)* MathieuSE(2*n + 1, q, (1)/(2)*Pi - z) |
MathieuC[2*n + 1, - q, z]=(- 1)^(n)* MathieuS[2*n + 1, q, Divide[1,2]*Pi - z] |
Failure | Failure | Successful | Fail
Complex[23.78813652597893, -3.3722327992542382] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[44.411224266286126, -43.54652180033389] <- {Rule[n, 2], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[31.14066048310312, -63.12632131709884] <- {Rule[n, 3], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8575002662710154, -10.873868123505298] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}} | MathieuSE(2*n + 1, - q, z)=(- 1)^(n)* MathieuCE(2*n + 1, q, (1)/(2)*Pi - z) |
MathieuS[2*n + 1, - q, z]=(- 1)^(n)* MathieuC[2*n + 1, q, Divide[1,2]*Pi - z] |
Failure | Failure | Successful | Fail
Complex[-2.359402591966014, 27.60697614269746] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[47.446183037810655, 46.79242964252569] <- {Rule[n, 2], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[63.57245907030711, 29.231688225822445] <- {Rule[n, 3], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-9.92152066646148, 3.1462660649328162] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.2.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}} | MathieuSE(2*n + 2, - q, z)=(- 1)^(n)* MathieuSE(2*n + 2, q, (1)/(2)*Pi - z) |
MathieuS[2*n + 2, - q, z]=(- 1)^(n)* MathieuS[2*n + 2, q, Divide[1,2]*Pi - z] |
Failure | Failure | Fail -33.89568074-158.8507182*I <- {q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-1663.167618+2486.508244*I <- {q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}50746.06591-21466.91354*I <- {q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}43.05202189+35.26439985*I <- {q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-13.013045011746364, -6.523555599290751] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[60.43374347015696, 35.92848167143245] <- {Rule[n, 2], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[80.47427800717344, 35.59929164615286] <- {Rule[n, 3], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.5195173062774003, 0.020895058047888604] <- {Rule[n, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 28.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{2n}@{z}{q} = \sum_{m=0}^{\infty}A^{2n}_{2m}(q)\cos@@{2mz}} | MathieuCE(2*n, q, z)sum(A(A[2*m])^(2*n)*(q)* cos(2*m*z), m = 0..infinity) |
MathieuC[2*n, q, z]Sum[A(Subscript[A, 2*m])^(2*n)*(q)* Cos[2*m*z], {m, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 28.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{2n+1}@{z}{q} = \sum_{m=0}^{\infty}A^{2n+1}_{2m+1}(q)\cos@@{(2m+1)z}} | MathieuCE(2*n + 1, q, z)sum(A(A[2*m + 1])^(2*n + 1)*(q)* cos((2*m + 1)* z), m = 0..infinity) |
MathieuC[2*n + 1, q, z]Sum[A(Subscript[A, 2*m + 1])^(2*n + 1)*(q)* Cos[(2*m + 1)* z], {m, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 28.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{2n+1}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+1}_{2m+1}(q)\sin@@{(2m+1)z}} | MathieuSE(2*n + 1, q, z)sum(B(B[2*m + 1])^(2*n + 1)*(q)* sin((2*m + 1)* z), m = 0..infinity) |
MathieuS[2*n + 1, q, z]Sum[B(Subscript[B, 2*m + 1])^(2*n + 1)*(q)* Sin[(2*m + 1)* z], {m, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 28.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{2n+2}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+2}_{2m+2}(q)\sin@@{(2m+2)z}} | MathieuSE(2*n + 2, q, z)sum(B(B[2*m + 2])^(2*n + 2)*(q)* sin((2*m + 2)* z), m = 0..infinity) |
MathieuS[2*n + 2, q, z]Sum[B(Subscript[B, 2*m + 2])^(2*n + 2)*(q)* Sin[(2*m + 2)* z], {m, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 28.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (C_{n}(q))^{2}\int_{0}^{2\pi}(f_{n}(x,q))^{2}\diff{x} = (S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x}} | (C[n]*(q))^(2)* int((f[n]*(x , q))^(2), x = 0..2*Pi)=(S[n]*(q))^(2)* int((g[n]*(x , q))^(2), x = 0..2*Pi) |
(Subscript[C, n]*(q))^(2)* Integrate[(Subscript[f, n]*(x , q))^(2), {x, 0, 2*Pi}]=(Subscript[S, n]*(q))^(2)* Integrate[(Subscript[g, n]*(x , q))^(2), {x, 0, 2*Pi}] |
Failure | Failure | Skip | Error |
| 28.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} = \pi} | (S[n]*(q))^(2)* int((g[n]*(x , q))^(2), x = 0..2*Pi)= Pi |
(Subscript[S, n]*(q))^(2)* Integrate[(Subscript[g, n]*(x , q))^(2), {x, 0, 2*Pi}]= Pi |
Failure | Failure | Skip | Error |
| 28.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \liminf_{n\to\infty}\frac{\rho_{n}^{(j)}}{n^{2}} >= kk^{\prime}(\compellintKk@{k})^{2}} | (rho(rho[n])^(j))/((n)^(2))> = k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2) |
Divide[\[Rho](Subscript[\[Rho], n])^(j),(n)^(2)]> = k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2) |
Failure | Failure | Skip | Successful |
| 28.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0} | sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity)= 0 |
Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}]= 0 |
Failure | Failure | Skip | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Sum[Plus[Times[-4, Power[n, 2]], MathieuCharacteristicA[Times[2, n], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Sum[Plus[Times[-4, Power[n, 2]], MathieuCharacteristicA[Times[2, n], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Sum[Plus[Times[-4, Power[n, 2]], MathieuCharacteristicA[Times[2, n], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Sum[Plus[Times[-4, Power[n, 2]], MathieuCharacteristicA[Times[2, n], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 28.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q} | sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity)= q |
Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}]= q |
Failure | Failure | Skip | Skip |
| 28.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q} | sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity)= - q |
Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}]= - q |
Failure | Failure | Skip | Skip |
| 28.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0} | sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity)= 0 |
Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}]= 0 |
Failure | Failure | Skip | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Sum[Plus[Times[-1, Power[Plus[2, Times[2, n]], 2]], MathieuCharacteristicB[Plus[2, Times[2, n]], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Sum[Plus[Times[-1, Power[Plus[2, Times[2, n]], 2]], MathieuCharacteristicB[Plus[2, Times[2, n]], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Sum[Plus[Times[-1, Power[Plus[2, Times[2, n]], 2]], MathieuCharacteristicB[Plus[2, Times[2, n]], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Sum[Plus[Times[-1, Power[Plus[2, Times[2, n]], 2]], MathieuCharacteristicB[Plus[2, Times[2, n]], q]], {n, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 28.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)} | (MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0))(W(W[m])^(+)*(x)*(P[m]*(x)- Q[m]*(x))+ W(W[m])^(-)*(x)*(P[m]*(x)+ Q[m]*(x))) |
Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]](W(Subscript[W, m])^(+)*(x)*(Subscript[P, m]*(x)- Subscript[Q, m]*(x))+ W(Subscript[W, m])^(-)*(x)*(Subscript[P, m]*(x)+ Subscript[Q, m]*(x))) |
Error | Failure | - | Error |
| 28.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)} | (MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) ))(W(W[m])^(+)*(x)*(P[m]*(x)- Q[m]*(x))- W(W[m])^(-)*(x)*(P[m]*(x)+ Q[m]*(x))) |
Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0](W(Subscript[W, m])^(+)*(x)*(Subscript[P, m]*(x)- Subscript[Q, m]*(x))- W(Subscript[W, m])^(-)*(x)*(Subscript[P, m]*(x)+ Subscript[Q, m]*(x))) |
Error | Failure | - | Error |
| 28.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}} | (2)/(Pi)*int(cos(2*h*cos(z)*cos(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2))(A(A[0])^(2*n)*((h)^(2)))/(MathieuCE(2*n, (h)^(2), (1)/(2)*Pi))*MathieuCE(2*n, (h)^(2), z) |
Divide[2,Pi]*Integrate[Cos[2*h*Cos[z]*Cos[t]]*MathieuC[2*n, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[A(Subscript[A, 0])^(2*n)*((h)^(2)),MathieuC[2*n, (h)^(2), Divide[1,2]*Pi]]*MathieuC[2*n, (h)^(2), z] |
Failure | Failure | Skip | Skip |
| 28.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{0}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}} | (2)/(Pi)*int(cosh(2*h*sin(z)*sin(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2))(A(A[0])^(2*n)*((h)^(2)))/(MathieuCE(2*n, (h)^(2), 0))*MathieuCE(2*n, (h)^(2), z) |
Divide[2,Pi]*Integrate[Cosh[2*h*Sin[z]*Sin[t]]*MathieuC[2*n, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[A(Subscript[A, 0])^(2*n)*((h)^(2)),MathieuC[2*n, (h)^(2), 0]]*MathieuC[2*n, (h)^(2), z] |
Failure | Failure | Skip | Skip |
| 28.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = -\frac{hA_{1}^{2n+1}(h^{2})}{\Mathieuce{2n+1}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}} | (2)/(Pi)*int(sin(2*h*cos(z)*cos(t))*MathieuCE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2))= (h*A(A[1])^(2*n + 1)*((h)^(2)))/(subs( temp=(1)/(2)*Pi, diff( MathieuCE(2*n + 1, (h)^(2), temp), temp$(1) ) ))*MathieuCE(2*n + 1, (h)^(2), z) |
Divide[2,Pi]*Integrate[Sin[2*h*Cos[z]*Cos[t]]*MathieuC[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}]= Divide[h*A(Subscript[A, 1])^(2*n + 1)*((h)^(2)),D[MathieuC[2*n + 1, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi]*MathieuC[2*n + 1, (h)^(2), z] |
Failure | Failure | Skip | Skip |
| 28.10.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = \frac{A_{1}^{2n+1}(h^{2})}{2\Mathieuce{2n+1}@{0}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}} | (2)/(Pi)*int(cos(z)*cos(t)*cosh(2*h*sin(z)*sin(t))*MathieuCE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2))(A(A[1])^(2*n + 1)*((h)^(2)))/(2*MathieuCE(2*n + 1, (h)^(2), 0))*MathieuCE(2*n + 1, (h)^(2), z) |
Divide[2,Pi]*Integrate[Cos[z]*Cos[t]*Cosh[2*h*Sin[z]*Sin[t]]*MathieuC[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[A(Subscript[A, 1])^(2*n + 1)*((h)^(2)),2*MathieuC[2*n + 1, (h)^(2), 0]]*MathieuC[2*n + 1, (h)^(2), z] |
Failure | Failure | Skip | Error |
| 28.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{hB_{1}^{2n+1}(h^{2})}{\Mathieuse{2n+1}'@{0}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}} | (2)/(Pi)*int(sinh(2*h*sin(z)*sin(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2))(h*B(B[1])^(2*n + 1)*((h)^(2)))/(subs( temp=0, diff( MathieuSE(2*n + 1, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 1, (h)^(2), z) |
Divide[2,Pi]*Integrate[Sinh[2*h*Sin[z]*Sin[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[h*B(Subscript[B, 1])^(2*n + 1)*((h)^(2)),D[MathieuS[2*n + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0]*MathieuS[2*n + 1, (h)^(2), z] |
Failure | Failure | Skip | Successful |
| 28.10.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{B_{1}^{2n+1}(h^{2})}{2\Mathieuse{2n+1}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}} | (2)/(Pi)*int(sin(z)*sin(t)*cos(2*h*cos(z)*cos(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2))(B(B[1])^(2*n + 1)*((h)^(2)))/(2*MathieuSE(2*n + 1, (h)^(2), (1)/(2)*Pi))*MathieuSE(2*n + 1, (h)^(2), z) |
Divide[2,Pi]*Integrate[Sin[z]*Sin[t]*Cos[2*h*Cos[z]*Cos[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[B(Subscript[B, 1])^(2*n + 1)*((h)^(2)),2*MathieuS[2*n + 1, (h)^(2), Divide[1,2]*Pi]]*MathieuS[2*n + 1, (h)^(2), z] |
Failure | Failure | Skip | Skip |
| 28.10.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = -\frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}} | (2)/(Pi)*int(sin(z)*sin(t)*sin(2*h*cos(z)*cos(t))*MathieuSE(2*n + 2, (h)^(2), t), t = 0..(Pi)/(2))= (h*B(B[2])^(2*n + 2)*((h)^(2)))/(2*subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*n + 2, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 2, (h)^(2), z) |
Divide[2,Pi]*Integrate[Sin[z]*Sin[t]*Sin[2*h*Cos[z]*Cos[t]]*MathieuS[2*n + 2, (h)^(2), t], {t, 0, Divide[Pi,2]}]= Divide[h*B(Subscript[B, 2])^(2*n + 2)*((h)^(2)),2*(D[MathieuS[2*n + 2, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi)]*MathieuS[2*n + 2, (h)^(2), z] |
Failure | Failure | Skip | Error |
| 28.10.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = \frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{0}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}} | (2)/(Pi)*int(cos(z)*cos(t)*sinh(2*h*sin(z)*sin(t))*MathieuSE(2*n + 2, (h)^(2), t), t = 0..(Pi)/(2))(h*B(B[2])^(2*n + 2)*((h)^(2)))/(2*subs( temp=0, diff( MathieuSE(2*n + 2, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 2, (h)^(2), z) |
Divide[2,Pi]*Integrate[Cos[z]*Cos[t]*Sinh[2*h*Sin[z]*Sin[t]]*MathieuS[2*n + 2, (h)^(2), t], {t, 0, Divide[Pi,2]}]Divide[h*B(Subscript[B, 2])^(2*n + 2)*((h)^(2)),2*(D[MathieuS[2*n + 2, (h)^(2), temp], {temp, 1}]/.temp-> 0)]*MathieuS[2*n + 2, (h)^(2), z] |
Failure | Failure | Skip | Error |
| 28.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = 2\sum_{n=0}^{\infty}A_{0}^{2n}(q)\Mathieuce{2n}@{z}{q}} | 1 = sum(A(A[0])^(2*n)*(q)* MathieuCE(2*n, q, z), n = 0..infinity) |
1 = Sum[A(Subscript[A, 0])^(2*n)*(q)* MathieuC[2*n, q, z], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 28.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{2mz} = \sum_{n=0}^{\infty}A_{2m}^{2n}(q)\Mathieuce{2n}@{z}{q}} | cos(2*m*z)sum(A(A[2*m])^(2*n)*(q)* MathieuCE(2*n, q, z), n = 0..infinity) |
Cos[2*m*z]Sum[A(Subscript[A, 2*m])^(2*n)*(q)* MathieuC[2*n, q, z], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 28.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{(2m+1)z} = \sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)\Mathieuce{2n+1}@{z}{q}} | cos((2*m + 1)* z)sum(A(A[2*m + 1])^(2*n + 1)*(q)* MathieuCE(2*n + 1, q, z), n = 0..infinity) |
Cos[(2*m + 1)* z]Sum[A(Subscript[A, 2*m + 1])^(2*n + 1)*(q)* MathieuC[2*n + 1, q, z], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 28.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{(2m+1)z} = \sum_{n=0}^{\infty}B_{2m+1}^{2n+1}(q)\Mathieuse{2n+1}@{z}{q}} | sin((2*m + 1)* z)sum(B(B[2*m + 1])^(2*n + 1)*(q)* MathieuSE(2*n + 1, q, z), n = 0..infinity) |
Sin[(2*m + 1)* z]Sum[B(Subscript[B, 2*m + 1])^(2*n + 1)*(q)* MathieuS[2*n + 1, q, z], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 28.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{(2m+2)z} = \sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\Mathieuse{2n+2}@{z}{q}} | sin((2*m + 2)* z)sum(B(B[2*m + 2])^(2*n + 2)*(q)* MathieuSE(2*n + 2, q, z), n = 0..infinity) |
Sin[(2*m + 2)* z]Sum[B(Subscript[B, 2*m + 2])^(2*n + 2)*(q)* MathieuS[2*n + 2, q, z], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 28.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu}@{z}{0} = e^{\iunit\nu z}} | Error |
Sqrt[2]*MathieuC[\[Nu], 0, z]= Exp[I*\[Nu]*z] |
Error | Failure | - | Error |
| 28.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\Mathieume{\nu}@{x}{q}\Mathieume{\nu}@{-x}{q}\diff{x} = \pi} | Error |
Integrate[Sqrt[2]*MathieuC[\[Nu], q, x]*Sqrt[2]*MathieuC[\[Nu], q, - x], {x, 0, Pi}]= Pi |
Error | Failure | - | Error |
| 28.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu}@{z+\pi}{q} = e^{\pi\iunit\nu}\Mathieume{\nu}@{z}{q}} | Error |
Sqrt[2]*MathieuC[\[Nu], q, z + Pi]= Exp[Pi*I*\[Nu]]*Sqrt[2]*MathieuC[\[Nu], q, z] |
Error | Failure | - | Error |
| 28.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{-\nu}@{z}{q} = \Mathieume{\nu}@{-z}{q}} | Error |
Sqrt[2]*MathieuC[- \[Nu], q, z]= Sqrt[2]*MathieuC[\[Nu], q, - z] |
Error | Failure | - | Error |
| 28.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu}@{z}{-q} = e^{\iunit\nu\pi/2}\Mathieume{\nu}@{z-\tfrac{1}{2}\pi}{q}} | Error |
Sqrt[2]*MathieuC[\[Nu], - q, z]= Exp[I*\[Nu]*Pi/ 2]*Sqrt[2]*MathieuC[\[Nu], q, z -Divide[1,2]*Pi] |
Error | Failure | - | Error |
| 28.12.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \conj{\Mathieume{\nu}@{z}{q}} = \Mathieume{\conj{\nu}}@{-\conj{z}}{\conj{q}}} | Error |
Conjugate[Sqrt[2]*MathieuC[\[Nu], q, z]]= Sqrt[2]*MathieuC[Conjugate[\[Nu]], Conjugate[q], - Conjugate[z]] |
Error | Failure | - | Error |
| 28.12#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{n}@{z}{q} = \sqrt{2}\Mathieuce{n}@{z}{q}} | Error |
Sqrt[2]*MathieuC[n, q, z]=Sqrt[2]*MathieuC[n, q, z] |
Error | Successful | - | - |
| 28.12#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{-n}@{z}{q} = -\sqrt{2}\iunit\Mathieuse{n}@{z}{q}} | Error |
Sqrt[2]*MathieuC[- n, q, z]= -Sqrt[2]*I*MathieuS[n, q, z] |
Error | Failure | - | Error |
| 28.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{\nu}@{z}{q} = \tfrac{1}{2}\left(\Mathieume{\nu}@{z}{q}+\Mathieume{\nu}@{-z}{q}\right)} | Error |
MathieuC[\[Nu], q, z]=Divide[1,2]*(Sqrt[2]*MathieuC[\[Nu], q, z]+ Sqrt[2]*MathieuC[\[Nu], q, - z]) |
Error | Failure | - | Error |
| 28.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{\nu}@{z}{q} = -\tfrac{1}{2}\iunit\left(\Mathieume{\nu}@{z}{q}-\Mathieume{\nu}@{-z}{q}\right)} | Error |
MathieuS[\[Nu], q, z]= -Divide[1,2]*I*(Sqrt[2]*MathieuC[\[Nu], q, z]- Sqrt[2]*MathieuC[\[Nu], q, - z]) |
Error | Failure | - | Error |
| 28.12.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{\nu}@{z}{q} = \Mathieuce{\nu}@{-z}{q}} | MathieuCE(nu, q, z)= MathieuCE(nu, q, - z) |
MathieuC[\[Nu], q, z]= MathieuC[\[Nu], q, - z] |
Successful | Successful | - | - |
| 28.12.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{\nu}@{-z}{q} = \Mathieuce{-\nu}@{z}{q}} | MathieuCE(nu, q, - z)= MathieuCE(- nu, q, z) |
MathieuC[\[Nu], q, - z]= MathieuC[- \[Nu], q, z] |
Failure | Failure | Error | Error |
| 28.12.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{\nu}@{z}{q} = -\Mathieuse{\nu}@{-z}{q}} | MathieuSE(nu, q, z)= - MathieuSE(nu, q, - z) |
MathieuS[\[Nu], q, z]= - MathieuS[\[Nu], q, - z] |
Successful | Successful | - | - |
| 28.12.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\Mathieuse{\nu}@{-z}{q} = -\Mathieuse{-\nu}@{z}{q}} | - MathieuSE(nu, q, - z)= - MathieuSE(- nu, q, z) |
- MathieuS[\[Nu], q, - z]= - MathieuS[- \[Nu], q, z] |
Failure | Failure | Error | Error |
| 28.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}} | Error |
Sqrt[2]*MathieuC[\[Nu], q, z]Sum[c(Subscript[c, 2*m])^(\[Nu])*(q)* Exp[I*(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 28.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z}} | MathieuCE(nu, q, z)sum(c(c[2*m])^(nu)*(q)* cos((nu + 2*m)* z), m = - infinity..infinity) |
MathieuC[\[Nu], q, z]Sum[c(Subscript[c, 2*m])^(\[Nu])*(q)* Cos[(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 28.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z}} | MathieuSE(nu, q, z)sum(c(c[2*m])^(nu)*(q)* sin((nu + 2*m)* z), m = - infinity..infinity) |
MathieuS[\[Nu], q, z]Sum[c(Subscript[c, 2*m])^(\[Nu])*(q)* Sin[(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 28.19.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\iunit\nu z} = \sum_{n=-\infty}^{\infty}c^{\nu+2n}_{-2n}(q)\Mathieume{\nu+2n}@{z}{q}} | Error |
Exp[I*\[Nu]*z]Sum[c(Subscript[c, - 2*n])^(\[Nu]+ 2*n)*(q)* Sqrt[2]*MathieuC[\[Nu]+ 2*n, q, z], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 28.22.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{\mathit{e},2m}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuce{2m}@{\frac{1}{2}\pi}{h^{2}}}{A_{0}^{2m}(h^{2})}} | g[exp(1), 2*m]*(h)=(- 1)^(m)*(MathieuCE(2*m, (h)^(2), (1)/(2)*Pi))/(A(A[0])^(2*m)*((h)^(2))) |
Subscript[g, E , 2*m]*(h)=(- 1)^(m)*Divide[MathieuC[2*m, (h)^(2), Divide[1,2]*Pi],A(Subscript[A, 0])^(2*m)*((h)^(2))] |
Failure | Failure | Error | Error |
| 28.22.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{\mathit{e},2m+1}(h) = (-1)^{m+1}\sqrt{\frac{2}{\pi}}\dfrac{\Mathieuce{2m+1}'@{\frac{1}{2}\pi}{h^{2}}}{hA_{1}^{2m+1}(h^{2})}} | g[exp(1), 2*m + 1]*(h)=(- 1)^(m + 1)*(subs( temp=(1)/(2)*Pi, diff( MathieuCE(2*m + 1, (h)^(2), temp), temp$(1) ) ))/(h*A(A[1])^(2*m + 1)*((h)^(2))) |
Subscript[g, E , 2*m + 1]*(h)=(- 1)^(m + 1)*Divide[D[MathieuC[2*m + 1, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,h*A(Subscript[A, 1])^(2*m + 1)*((h)^(2))] |
Failure | Failure | Error | Error |
| 28.22.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{\mathit{o},2m+1}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+1}@{\frac{1}{2}\pi}{h^{2}}}{hB_{1}^{2m+1}(h^{2})}} | g[o , 2*m + 1]*(h)=(- 1)^(m)*(MathieuSE(2*m + 1, (h)^(2), (1)/(2)*Pi))/(h*B(B[1])^(2*m + 1)*((h)^(2))) |
Subscript[g, o , 2*m + 1]*(h)=(- 1)^(m)*Divide[MathieuS[2*m + 1, (h)^(2), Divide[1,2]*Pi],h*B(Subscript[B, 1])^(2*m + 1)*((h)^(2))] |
Failure | Failure | Error | Error |
| 28.22.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{\mathit{o},2m+2}(h) = (-1)^{m+1}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+2}'@{\frac{1}{2}\pi}{h^{2}}}{h^{2}B_{2}^{2m+2}(h^{2})}} | g[o , 2*m + 2]*(h)=(- 1)^(m + 1)*(subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*m + 2, (h)^(2), temp), temp$(1) ) ))/((h)^(2)* B(B[2])^(2*m + 2)*((h)^(2))) |
Subscript[g, o , 2*m + 2]*(h)=(- 1)^(m + 1)*Divide[D[MathieuS[2*m + 2, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,(h)^(2)* B(Subscript[B, 2])^(2*m + 2)*((h)^(2))] |
Failure | Failure | Error | Error |
| 28.25.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0} | (m + 1)* (D[m + 1])^(+)+((m +(1)/(2))^(2)+(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)* (D[m])^(+)+(m -(1)/(2))*(8*I*h*m)* (D[m - 1])^(+)= 0 |
(m + 1)* (Subscript[D, m + 1])^(+)+((m +Divide[1,2])^(2)+(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)* (Subscript[D, m])^(+)+(m -Divide[1,2])*(8*I*h*m)* (Subscript[D, m - 1])^(+)= 0 |
Error | Failure | - | Error |
| 28.25.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0} | (m + 1)* (D[m + 1])^(-)+((m +(1)/(2))^(2)-(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)* (D[m])^(-)-(m -(1)/(2))*(8*I*h*m)* (D[m - 1])^(-)= 0 |
(m + 1)* (Subscript[D, m + 1])^(-)+((m +Divide[1,2])^(2)-(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)* (Subscript[D, m])^(-)-(m -Divide[1,2])*(8*I*h*m)* (Subscript[D, m - 1])^(-)= 0 |
Error | Failure | - | Error |
| 28.26.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi = 2h\sinh@@{z}-\left(m+\tfrac{1}{2}\right)\atan@{\sinh@@{z}}} | phi = 2*h*sinh(z)-(m +(1)/(2))* arctan(sinh(z)) |
\[Phi]= 2*h*Sinh[z]-(m +Divide[1,2])* ArcTan[Sinh[z]] |
Failure | Failure | Fail 8.881737466-4.791146621*I <- {h = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}10.37211930-4.302072204*I <- {h = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}11.86250114-3.812997788*I <- {h = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-3.289185494+5.912553089*I <- {h = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Error |
| 28.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \cosh@@{z}\cos@@{t}\cos@@{\alpha}+\sinh@@{z}\sin@@{t}\sin@@{\alpha}} | w = cosh(z)*cos(t)*cos(alpha)+ sinh(z)*sin(t)*sin(alpha) |
w = Cosh[z]*Cos[t]*Cos[\[Alpha]]+ Sinh[z]*Sin[t]*Sin[\[Alpha]] |
Failure | Failure | Fail 1.558413509-1.537727303*I <- {alpha = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.934763107+4.464613324*I <- {alpha = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.290314455+18.77347892*I <- {alpha = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}9.261119835-14.27924254*I <- {alpha = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \phase@{h(\cosh@@{z}+ 1)}} | 0 < argument(h*(cosh(z)+ 1)) |
0 < Arg[h*(Cosh[z]+ 1)] |
Failure | Failure | Fail 0. < -.1740759484 <- {h = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}0. < -.1740759484 <- {h = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}0. < -1.744872276 <- {h = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}0. < -1.744872276 <- {h = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \phase@{h(\cosh@@{z}- 1)}} | 0 < argument(h*(cosh(z)- 1)) |
0 < Arg[h*(Cosh[z]- 1)] |
Failure | Failure | Fail 0. < -1.118030274 <- {h = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}0. < -1.118030274 <- {h = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}0. < -2.688826601 <- {h = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}0. < -2.688826601 <- {h = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{h(\cosh@@{z}+ 1)} < \pi} | argument(h*(cosh(z)+ 1))< Pi |
Arg[h*(Cosh[z]+ 1)]< Pi |
Failure | Failure | Skip | Error |
| 28.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{h(\cosh@@{z}- 1)} < \pi} | argument(h*(cosh(z)- 1))< Pi |
Arg[h*(Cosh[z]- 1)]< Pi |
Failure | Failure | Skip | Error |
| 28.28#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R(z,t) = \left(\tfrac{1}{2}(\cosh@{2z}+\cos@{2t})\right)^{\ifrac{1}{2}}} | R*(z , t)=((1)/(2)*(cosh(2*z)+ cos(2*t)))^((1)/(2)) |
R*(z , t)=(Divide[1,2]*(Cosh[2*z]+ Cos[2*t]))^(Divide[1,2]) |
Failure | Failure | Error | Error |
| 28.28#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R(z,0) = \cosh@@{z}} | R*(z , 0)= cosh(z) |
R*(z , 0)= Cosh[z] |
Failure | Failure | Error | Error |
| 28.28#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{2\iunit\phi} = \dfrac{\cosh@{z+\iunit t}}{\cosh@{z-\iunit t}}} | exp(2*I*phi)=(cosh(z + I*t))/(cosh(z - I*t)) |
Exp[2*I*\[Phi]]=Divide[Cosh[z + I*t],Cosh[z - I*t]] |
Failure | Failure | Fail .5583951073e-1+.1820881038e-1*I <- {phi = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.5598730513e-1-.1787687390e-1*I <- {phi = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}8.866720637+.1820881038e-1*I <- {phi = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}8.019859366+2.615210924*I <- {phi = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.28.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha^{(1)}_{\nu,m} = \dfrac{1}{2\pi}\int_{0}^{2\pi}\sin@@{t}\Mathieume{\nu}@{t}{h^{2}}\Mathieume{-\nu-2m-1}@{t}{h^{2}}\diff{t}} | Error |
(Subscript[\[Alpha], \[Nu], m])^(1)=Divide[1,2*Pi]*Integrate[Sin[t]*Sqrt[2]*MathieuC[\[Nu], (h)^(2), t]*Sqrt[2]*MathieuC[- \[Nu]- 2*m - 1, (h)^(2), t], {t, 0, 2*Pi}] |
Error | Failure | - | Error |
| 28.29.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}Q(z)\diff{z} = 0} | int(Q*(z), z = 0..Pi)= 0 |
Integrate[Q*(z), {z, 0, Pi}]= 0 |
Failure | Failure | Skip | Error |
| 28.29.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 < \realpart@@{\nu}} | - 1 < Re(nu) |
- 1 < Re[\[Nu]] |
Failure | Failure | Fail -1. < -1.414213562 <- {nu = -2^(1/2)-I*2^(1/2)}-1. < -1.414213562 <- {nu = -2^(1/2)+I*2^(1/2)} |
Error |
| 28.29.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\nu} <= 1} | Re(nu)< = 1 |
Re[\[Nu]]< = 1 |
Failure | Failure | Fail 1.414213562 <= 1. <- {nu = 2^(1/2)+I*2^(1/2)}1.414213562 <= 1. <- {nu = 2^(1/2)-I*2^(1/2)} |
Error |
| 28.29.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+\pi) = e^{\pi\iunit\nu}w(z)} | w*(z + Pi)= exp(Pi*I*nu)*w*(z) |
w*(z + Pi)= Exp[Pi*I*\[Nu]]*w*(z) |
Failure | Failure | Fail 4.397533327+8.455409696*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}8.455409696+4.488232549*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}4.488232549+.4303561791*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.4303561791+4.397533327*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.29.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)} | w*(z + Pi)+ w*(z - Pi)= 2*cos(Pi*nu)*w*(z) |
w*(z + Pi)+ w*(z - Pi)= 2*Cos[Pi*\[Nu]]*w*(z) |
Failure | Failure | Fail 327.7574484+98.56031892*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}98.56031892-327.7574484*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-327.7574484-98.56031892*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-98.56031892+327.7574484*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.30.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{0}^{2\pi}w_{m}(x)w_{n}(x)\diff{x} = \Kroneckerdelta{m}{n}} | (1)/(2*Pi)*int(w[m]*(x)* w[n]*(x), x = 0..2*Pi)= KroneckerDelta[m, n] |
Divide[1,2*Pi]*Integrate[Subscript[w, m]*(x)* Subscript[w, n]*(x), {x, 0, 2*Pi}]= KroneckerDelta[m, n] |
Failure | Failure | Skip | Error |
| 28.31#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(z) = w(z)\exp@{-\tfrac{1}{4}\xi\cos@{2z}}} | W*(z)= w*(z)* exp(-(1)/(4)*xi*cos(2*z)) |
W*(z)= w*(z)* Exp[-Divide[1,4]*\[Xi]*Cos[2*z]] |
Failure | Failure | Fail -16.39510758+26.39608289*I <- {W = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}66.37576538-162.5747100*I <- {W = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}16.39510758-26.39608289*I <- {W = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-66.37576538+162.5747100*I <- {W = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.31.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{\mathit{e},s}(z) = \sum_{\ell=0}^{\infty}A_{2\ell+s}\cos@@{(2\ell+s)z}} | w[exp(1), s]*(z)= sum(A[2*ell + s]*cos((2*ell + s)* z), ell = 0..infinity) |
Subscript[w, E , s]*(z)= Sum[Subscript[A, 2*\[ScriptL]+ s]*Cos[(2*\[ScriptL]+ s)* z], {\[ScriptL], 0, Infinity}] |
Error | Failure | - | Error |
| 28.31.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{\mathit{o},s}(z) = \sum_{\ell=0}^{\infty}B_{2\ell+s}\sin@@{(2\ell+s)z}} | w[o , s]*(z)= sum(B[2*ell + s]*sin((2*ell + s)* z), ell = 0..infinity) |
Subscript[w, o , s]*(z)= Sum[Subscript[B, 2*\[ScriptL]+ s]*Sin[(2*\[ScriptL]+ s)* z], {\[ScriptL], 0, Infinity}] |
Error | Failure | - | Error |
| 28.31.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\diff{x} = \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x}} | int((C(C[p])^(m)*(x , xi))^(2), x = 0..2*Pi)=int((S(S[p])^(m)*(x , xi))^(2), x = 0..2*Pi) |
Integrate[(C(Subscript[C, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}]=Integrate[(S(Subscript[S, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}] |
Failure | Failure | Skip | Error |
| 28.31.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x} = 1} | int((S(S[p])^(m)*(x , xi))^(2), x = 0..2*Pi)= 1 |
Integrate[(S(Subscript[S, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}]= 1 |
Failure | Failure | Skip | Error |
| 28.31.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\mathit{hc}_{p}^{m_{1}}(x,\xi)\mathit{hc}_{p}^{m_{2}}(x,\xi)\diff{x} = \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x}} | int(h*s(s[p])^(m[1])*(x , xi)* h*s(s[p])^(m[2])*(x , xi), x = 0..2*Pi) |
Integrate[h*s(Subscript[s, p])^(Subscript[m, 1])*(x , \[Xi])* h*s(Subscript[s, p])^(Subscript[m, 2])*(x , \[Xi]), {x, 0, 2*Pi}] |
Failure | Failure | Skip | Error |
| 28.31.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x} = 0} | int(h*s(s[p])^(m[1])*(x , xi)* h*s(s[p])^(m[2])*(x , xi), x = 0..2*Pi)= 0 |
Integrate[h*s(Subscript[s, p])^(Subscript[m, 1])*(x , \[Xi])* h*s(Subscript[s, p])^(Subscript[m, 2])*(x , \[Xi]), {x, 0, 2*Pi}]= 0 |
Failure | Failure | Skip | Error |
| 28.31.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0} | int(int(h*c(c[p[1]])^(m[1])*(u , xi)* h*c(c[p[1]])^(m[1])*(v , xi)* h*c(c[p[2]])^(m[2])*(u , xi)* h*c(c[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity])= 0 |
Integrate[Integrate[h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*c(Subscript[c, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*c(Subscript[c, Subscript[p, 2]])^(Subscript[m, 2])*(v , \[Xi])*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}], {u, Subscript[u, 0], Subscript[u, Infinity]}]= 0 |
Failure | Failure | Skip | Error |
| 28.31.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0} | int(int(h*s(s[p[1]])^(m[1])*(u , xi)* h*s(s[p[1]])^(m[1])*(v , xi)* h*s(s[p[2]])^(m[2])*(u , xi)* h*s(s[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity])= 0 |
Integrate[Integrate[h*s(Subscript[s, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*s(Subscript[s, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(v , \[Xi])*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}], {u, Subscript[u, 0], Subscript[u, Infinity]}]= 0 |
Failure | Failure | Skip | Error |
| 28.31.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0} | int(int(h*c(c[p[1]])^(m[1])*(u , xi)* h*c(c[p[1]])^(m[1])*(v , xi)* h*s(s[p[2]])^(m[2])*(u , xi)* h*s(s[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity])= 0 |
Integrate[Integrate[h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(v , \[Xi])*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}], {u, Subscript[u, 0], Subscript[u, Infinity]}]= 0 |
Failure | Failure | Skip | Error |
| 28.32#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = c\cosh@@{\xi}\cos@@{\eta}} | x = c*cosh(xi)*cos(eta) |
x = c*Cosh[\[Xi]]*Cos[\[Eta]] |
Failure | Failure | Fail -4.329890955-5.329890955*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 1}-3.329890955-5.329890955*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 2}-2.329890955-5.329890955*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 3}4.167193694+6.839909304*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Error |
| 28.32#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = c\sinh@@{\xi}\sin@@{\eta}} | y = c*sinh(xi)*sin(eta) |
y = c*Sinh[\[Xi]]*Sin[\[Eta]] |
Failure | Failure | Fail 7.675321591-6.675321591*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 3}-7.254122865+4.581407255*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), y = 1}... skip entries to safe data |
Error |
| 28.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{V}{x}+\pderiv[2]{V}{y}+k^{2}V = 0} | diff(V, [x$(2)])+ diff(V, [y$(2)])+ (k)^(2)* V = 0 |
D[V, {x, 2}]+ D[V, {y, 2}]+ (k)^(2)* V = 0 |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {V = 2^(1/2)+I*2^(1/2), k = 1}5.656854248+5.656854248*I <- {V = 2^(1/2)+I*2^(1/2), k = 2}12.72792206+12.72792206*I <- {V = 2^(1/2)+I*2^(1/2), k = 3}1.414213562-1.414213562*I <- {V = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Error |
| 28.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{V}{\xi}+\pderiv[2]{V}{\eta}+\frac{1}{2}c^{2}k^{2}(\cosh@{2\xi}-\cos@{2\eta})V = 0} | diff(V, [xi$(2)])+ diff(V, [eta$(2)])+(1)/(2)*(c)^(2)* (k)^(2)*(cosh(2*xi)- cos(2*eta))* V = 0 |
D[V, {\[Xi], 2}]+ D[V, {\[Eta], 2}]+Divide[1,2]*(c)^(2)* (k)^(2)*(Cosh[2*\[Xi]]- Cos[2*\[Eta]])* V = 0 |
Failure | Failure | Fail -14.69086244-14.69086244*I <- {V = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 1}-58.76344974-58.76344974*I <- {V = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 2}-132.2177619-132.2177619*I <- {V = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 3}-14.69086244-14.69086244*I <- {V = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Error |
| 28.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{K}{z}-\pderiv[2]{K}{\zeta} = 2q\left(\cos@{2z}-\cos@{2\zeta}\right)K} | diff(K, [z$(2)])- diff(K, [zeta$(2)])= 2*q*(cos(2*z)- cos(2*zeta))* K |
D[K, {z, 2}]- D[K, {\[zeta], 2}]= 2*q*(Cos[2*z]- Cos[2*\[zeta]])* K |
Failure | Failure | Fail -41.55203380-0.*I <- {K = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}-41.55203380-0.*I <- {K = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}41.55203380-0.*I <- {K = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}41.55203380-0.*I <- {K = 2^(1/2)+I*2^(1/2), q = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
Error |
| 28.32#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{1} = \tfrac{1}{2}c\left(\cosh@{2\alpha}+\cos@{2\beta}-\cosh@{2\gamma}\right)} | x[1]=(1)/(2)*c*(cosh(2*alpha)+ cos(2*beta)- cosh(2*gamma)) |
Subscript[x, 1]=Divide[1,2]*c*(Cosh[2*\[Alpha]]+ Cos[2*\[Beta]]- Cosh[2*\[Gamma]]) |
Failure | Failure | Fail 14.06853191+14.06853191*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[1] = 2^(1/2)+I*2^(1/2)}14.06853191+11.24010479*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[1] = 2^(1/2)-I*2^(1/2)}11.24010479+11.24010479*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[1] = -2^(1/2)-I*2^(1/2)}11.24010479+14.06853191*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[1] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{2} = 2c\cosh@@{\alpha}\cos@@{\beta}\sinh@@{\gamma}} | x[2]= 2*c*cosh(alpha)*cos(beta)*sinh(gamma) |
Subscript[x, 2]= 2*c*Cosh[\[Alpha]]*Cos[\[Beta]]*Sinh[\[Gamma]] |
Failure | Failure | Fail -5.086190384-5.086190384*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[2] = 2^(1/2)+I*2^(1/2)}-5.086190384-7.914617508*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[2] = 2^(1/2)-I*2^(1/2)}-7.914617508-7.914617508*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[2] = -2^(1/2)-I*2^(1/2)}-7.914617508-5.086190384*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[2] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.32#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{3} = 2c\sinh@@{\alpha}\sin@@{\beta}\cosh@@{\gamma}} | x[3]= 2*c*sinh(alpha)*sin(beta)*cosh(gamma) |
Subscript[x, 3]= 2*c*Sinh[\[Alpha]]*Sin[\[Beta]]*Cosh[\[Gamma]] |
Failure | Failure | Fail 17.05136734-14.22294022*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[3] = 2^(1/2)+I*2^(1/2)}17.05136734-17.05136734*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[3] = 2^(1/2)-I*2^(1/2)}14.22294022-17.05136734*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[3] = -2^(1/2)-I*2^(1/2)}14.22294022-14.22294022*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x[3] = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Error |
| 28.33.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{W}{x}+\pderiv[2]{W}{y}-\frac{\rho}{\tau}\pderiv[2]{W}{t} = 0} | diff(W, [x$(2)])+ diff(W, [y$(2)])-(rho)/(tau)*diff(W, [t$(2)])= 0 |
D[W, {x, 2}]+ D[W, {y, 2}]-Divide[\[Rho],\[Tau]]*D[W, {t, 2}]= 0 |
Successful | Successful | - | - |