Results of Lamé Functions

From DRMF
Jump to navigation Jump to search
DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
29.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k})w = 0} diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2))* w = 0 D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2))* w = 0 Failure Failure
Fail
7.948739768-7.545139452*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}
51.95468921+27.97388965*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}
-3.910915794-11.82960931*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}
6.183103152-8.579425434*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
29.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{\xi}+\frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)\deriv{w}{\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi-k^{-2})}w = 0} diff(w, [xi$(2)])+(1)/(2)*((1)/(xi)+(1)/(xi - 1)+(1)/(xi - (k)^(- 2)))* diff(w, xi)+(h*(k)^(- 2)- nu*(nu + 1)* xi)/(4*xi*(xi - 1)*(xi - (k)^(- 2)))*w = 0 D[w, {\[Xi], 2}]+Divide[1,2]*(Divide[1,\[Xi]]+Divide[1,\[Xi]- 1]+Divide[1,\[Xi]- (k)^(- 2)])* D[w, \[Xi]]+Divide[h*(k)^(- 2)- \[Nu]*(\[Nu]+ 1)* \[Xi],4*\[Xi]*(\[Xi]- 1)*(\[Xi]- (k)^(- 2))]*w = 0 Failure Failure
Fail
-1.197364586+.3597957455*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 1}
-1.025513349+.2414101023e-1*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 2}
-.9825277432-.7730059408e-2*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 3}
.1006999677+1.062488515*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
29.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-k^{2}\cos^{2}@@{\phi})\deriv[2]{w}{\phi}+k^{2}\cos@@{\phi}\sin@@{\phi}\deriv{w}{\phi}+(h-\nu(\nu+1)k^{2}\cos^{2}@@{\phi})w = 0} (1 - (k)^(2)* (cos(phi))^(2))* diff(w, [phi$(2)])+ (k)^(2)* cos(phi)*sin(phi)*diff(w, phi)+(h - nu*(nu + 1)*(k)^(2)* (cos(phi))^(2))* w = 0 (1 - (k)^(2)* (Cos[\[Phi]])^(2))* D[w, {\[Phi], 2}]+ (k)^(2)* Cos[\[Phi]]*Sin[\[Phi]]*D[w, \[Phi]]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (Cos[\[Phi]])^(2))* w = 0 Failure Failure
Fail
-32.55364142+30.82095554*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 1}
-130.2145657+111.2838222*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 2}
-292.9827729+245.3885999*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 3}
30.82095554+32.55364142*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
29.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\deriv[2]{w}{\zeta}+\frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_{3}}\right)\deriv{w}{\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(\zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w = 0} diff(w, [zeta$(2)])+(1)/(2)*((1)/(zeta - e[1])+(1)/(zeta - e[2])+(1)/(zeta - e[3]))* diff(w, zeta)+(g - nu*(nu + 1)* zeta)/(4*(zeta - e[1])*(zeta - e[2])*(zeta - e[3]))*w = 0 D[w, {\[zeta], 2}]+Divide[1,2]*(Divide[1,\[zeta]- Subscript[e, 1]]+Divide[1,\[zeta]- Subscript[e, 2]]+Divide[1,\[zeta]- Subscript[e, 3]])* D[w, \[zeta]]+Divide[g - \[Nu]*(\[Nu]+ 1)* \[zeta],4*(\[zeta]- Subscript[e, 1])*(\[zeta]- Subscript[e, 2])*(\[zeta]- Subscript[e, 3])]*w = 0 Failure Failure Skip Error
29.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = k^{2}\Jacobiellsnk@{z}{k}\Jacobiellsnk@{z_{1}}{k}\Jacobiellsnk@{z_{2}}{k}\Jacobiellsnk@{z_{3}}{k}-\frac{k^{2}}{{k^{\prime}}^{2}}\Jacobiellcnk@{z}{k}\Jacobiellcnk@{z_{1}}{k}\Jacobiellcnk@{z_{2}}{k}\Jacobiellcnk@{z_{3}}{k}+\frac{1}{{k^{\prime}}^{2}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}\Jacobielldnk@{z_{2}}{k}\Jacobielldnk@{z_{3}}{k}} x = (k)^(2)* JacobiSN(z, k)*JacobiSN(z[1], k)*JacobiSN(z[2], k)*JacobiSN(z[3], k)-((k)^(2))/(1 - (k)^(2))*JacobiCN(z, k)*JacobiCN(z[1], k)*JacobiCN(z[2], k)*JacobiCN(z[3], k)+(1)/(1 - (k)^(2))*JacobiDN(z, k)*JacobiDN(z[1], k)*JacobiDN(z[2], k)*JacobiDN(z[3], k) x = (k)^(2)* JacobiSN[z, (k)^2]*JacobiSN[Subscript[z, 1], (k)^2]*JacobiSN[Subscript[z, 2], (k)^2]*JacobiSN[Subscript[z, 3], (k)^2]-Divide[(k)^(2),1 - (k)^(2)]*JacobiCN[z, (k)^2]*JacobiCN[Subscript[z, 1], (k)^2]*JacobiCN[Subscript[z, 2], (k)^2]*JacobiCN[Subscript[z, 3], (k)^2]+Divide[1,1 - (k)^(2)]*JacobiDN[z, (k)^2]*JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2] Failure Failure Skip Successful
29.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu w(z_{1})w(z_{2})w(z_{3}) = \int_{-2\!\compellintKk@@{k}\!}^{2\!\compellintKk@@{k}\!}\FerrersP[]{\nu}@{x}w(z)\diff{z}} mu*w*(z[1])* w*(z[2])* w*(z[3])= int(LegendreP(nu, x)*w*(z), z = - 2*EllipticK(k)..2*EllipticK(k)) \[Mu]*w*(Subscript[z, 1])* w*(Subscript[z, 2])* w*(Subscript[z, 3])= Integrate[LegendreP[\[Nu], x]*w*(z), {z, - 2*EllipticK[(k)^2], 2*EllipticK[(k)^2]}] Failure Failure - Skip
29.8#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+2\!\compellintKk@@{k}\!) = \sigma w(z)} w*(z + 2*EllipticK(k))= sigma*w*(z) w*(z + 2*EllipticK[(k)^2])= \[Sigma]*w*(z) Failure Failure Error
Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.090638940207405, -2.3226169111049417] <- {Rule[k, 2], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.565752102125508, -2.5159784259617144] <- {Rule[k, 3], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[k, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
29.8#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z+2\!\compellintKk@@{k}\!) = \tau w(z)+\sigma w_{2}(z)} w[2]*(z + 2*EllipticK(k))= tau*w*(z)+ sigma*w[2]*(z) Subscript[w, 2]*(z + 2*EllipticK[(k)^2])= \[Tau]*w*(z)+ \[Sigma]*Subscript[w, 2]*(z) Failure Failure Skip Skip
29.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \frac{1}{k^{\prime}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}} y =(1)/(sqrt(1 - (k)^(2)))*JacobiDN(z, k)*JacobiDN(z[1], k) y =Divide[1,Sqrt[1 - (k)^(2)]]*JacobiDN[z, (k)^2]*JacobiDN[Subscript[z, 1], (k)^2] Failure Failure
Fail
Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 1}
Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 2}
Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 3}
3.937738242+.2897798728*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 2, y = 1}
... skip entries to safe data
Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[k, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[k, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[k, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
29.11.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0} diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2)+ (k)^(2)* (omega)^(2)* (JacobiSN(z, k))^(4))* w = 0 D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (k)^(2)* (\[Omega])^(2)* (JacobiSN[z, (k)^2])^(4))* w = 0 Failure Failure Skip Skip
29.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(s,t) = \Jacobiellsnk^{2}@{\!\compellintKk@@{k}\!+\iunit t}{k}-\Jacobiellsnk^{2}@{s}{k}} w*(s , t)= (JacobiSN(EllipticK(k)+ I*t, k))^(2)- (JacobiSN(s, k))^(2) w*(s , t)= (JacobiSN[EllipticK[(k)^2]+ I*t, (k)^2])^(2)- (JacobiSN[s, (k)^2])^(2) Failure Failure Error Error
29.17.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F(z) = E(z)\int_{\iunit\!\ccompellintKk@@{k}\!}^{z}\frac{\diff{u}}{(E(u))^{2}}} F*(z)= E*(z)* int((1)/((E*(u))^(2)), u = I*EllipticCK(k)..z) F*(z)= E*(z)* Integrate[Divide[1,(E*(u))^(2)], {u, I*EllipticK[1-(k)^2], z}] Failure Failure Skip
Fail
Complex[0.03667157790603448, 4.331207863265408] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.11462120344581403, 4.482500644617256] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.2493650915526525, 4.6172445327240945] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.69908730443685, 0.33120786326540785] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
29.18#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = kr\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}} x = k*r*JacobiSN(beta, k)*JacobiSN(gamma, k) x = k*r*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2] Failure Failure
Fail
.2066406870-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 1}
1.206640687-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 2}
2.206640687-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 3}
.9014522664-2.018283670*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 2, x = 1}
... skip entries to safe data
 Skip
29.18#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \iunit\frac{k}{k^{\prime}}r\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}} y = I*(k)/(sqrt(1 - (k)^(2)))*r*JacobiCN(beta, k)*JacobiCN(gamma, k) y = I*Divide[k,Sqrt[1 - (k)^(2)]]*r*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2] Failure Failure
Fail
Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 1}
Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 2}
Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 3}
3.451665915+.7621257589*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 2, y = 1}
... skip entries to safe data
 Skip
29.18#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{1}{k^{\prime}}r\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}} z =(1)/(sqrt(1 - (k)^(2)))*r*JacobiDN(beta, k)*JacobiDN(gamma, k) z =Divide[1,Sqrt[1 - (k)^(2)]]*r*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2] Failure Failure
Fail
Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}
1.356638323+2.584421950*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}
1.490898086+1.415864964*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}
Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
29.18#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 <= \gamma} 0 < = gamma 0 < = \[Gamma] Failure Failure Successful Successful
29.18#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma <= 4\!\compellintKk@@{k}\!} gamma < = 4*EllipticK(k) \[Gamma]< = 4*EllipticK[(k)^2] Failure Failure Error Successful
29.18.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{r}\left(r^{2}\deriv{u_{1}}{r}\right)+(\omega^{2}r^{2}-\nu(\nu+1))u_{1} = 0} diff(((r)^(2)* diff(u[1], r))+((omega)^(2)* (r)^(2)- nu*(nu + 1))* u[1], r)= 0 D[((r)^(2)* D[Subscript[u, 1], r])+((\[Omega])^(2)* (r)^(2)- \[Nu]*(\[Nu]+ 1))* Subscript[u, 1], r]= 0 Failure Failure
Fail
-31.99999996+0.*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = 2^(1/2)+I*2^(1/2)}
0.+31.99999996*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = 2^(1/2)-I*2^(1/2)}
31.99999996+0.*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = -2^(1/2)-I*2^(1/2)}
0.-31.99999996*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
-32.0 <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 32.0] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
32.0 <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -32.0] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
29.18.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u_{2}}{\beta}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\beta}{k})u_{2} = 0} diff(u[2], [beta$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(beta, k))^(2))* u[2]= 0 D[Subscript[u, 2], {\[Beta], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Beta], (k)^2])^(2))* Subscript[u, 2]= 0 Failure Failure
Fail
7.948739768-7.545139452*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 1}
51.95468921+27.97388965*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 2}
-3.910915794-11.82960931*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 3}
-7.545139452-7.948739768*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
29.18.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u_{3}}{\gamma}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\gamma}{k})u_{3} = 0} diff(u[3], [gamma$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(gamma, k))^(2))* u[3]= 0 D[Subscript[u, 3], {\[Gamma], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Gamma], (k)^2])^(2))* Subscript[u, 3]= 0 Error Failure - Skip
29.18#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = k\Jacobiellsnk@{\alpha}{k}\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}} x = k*JacobiSN(alpha, k)*JacobiSN(beta, k)*JacobiSN(gamma, k) x = k*JacobiSN[\[Alpha], (k)^2]*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2] Failure Failure
Fail
.3496751872-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 1}
1.349675187-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 2}
2.349675187-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 3}
.8887187920-1.136817507*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 2, x = 1}
... skip entries to safe data
 Skip
29.18#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = -\frac{k}{k^{\prime}}\Jacobiellcnk@{\alpha}{k}\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}} y = -(k)/(sqrt(1 - (k)^(2)))*JacobiCN(alpha, k)*JacobiCN(beta, k)*JacobiCN(gamma, k) y = -Divide[k,Sqrt[1 - (k)^(2)]]*JacobiCN[\[Alpha], (k)^2]*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2] Failure Failure
Fail
Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 1}
Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 2}
Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 3}
-.314074508-.9043815133*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 2, y = 1}
... skip entries to safe data
 Skip
29.18#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{\iunit}{kk^{\prime}}\Jacobielldnk@{\alpha}{k}\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}} z =(I)/(k*sqrt(1 - (k)^(2)))*JacobiDN(alpha, k)*JacobiDN(beta, k)*JacobiDN(gamma, k) z =Divide[I,k*Sqrt[1 - (k)^(2)]]*JacobiDN[\[Alpha], (k)^2]*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2] Failure Failure
Fail
Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}
1.349197762+2.073332495*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}
1.413658462+1.427095902*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}
Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
 Skip
Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Results_of_Lamé_Functions&oldid=63480"