DLMF Results: Difference between revisions
Jump to navigation
Jump to search
Created page with "{| class="wikitable sortable" |- ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica |- | [..." |
No edit summary |
||
| Line 3: | Line 3: | ||
! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ||
|- | |- | ||
| [[Item:Q30|1.2.E1]] | | | [[Item:Q30|1.2.E1]] || <math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math> || <code>binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k))</code> || <code>Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [[Item: | | [[Item:Q30|1.2.E1]] || <math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math> || <code>(factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k)</code> || <code>Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k]</code> || Successful || Successful || - || - | ||
|- | |||
| [[Item:Q35|1.2.E6]] || <math>\binom{z}{k} = \frac{z(z-1)\cdots(z-k+1)}{k!}</math> || <code>binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k))</code> || <code>Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!]</code> || Successful || Successful || - || - | |||
|- | |||
| [[Item:Q36|1.2.E7]] || <math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math> || <code>binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1)</code> || <code>Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1]</code> || Successful || Successful || - || - | |||
|- | |||
| [[Item:Q37|1.2.E8]] || <math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math> || <code>sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m)</code> || <code>Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m]</code> || Successful || Successful || - || - | |||
|- | |||
| [[Item:Q87|1.4.E8]] || <math>f^{(2)}(x) = \deriv[2]{f}{x}</math> || <code>(f)^(2)*(x)= diff(f, [x$(2)])</code> || <code>(f)^(2)*(x)= D[f, {x, 2}]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br></div></div> | |||
|- | |||
| [[Item:Q87|1.4.E8]] || <math>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</math> || <code>diff(f, [x$(2)])= diff(diff(f, x), x)</code> || <code>D[f, {x, 2}]= D[D[f, x], x]</code> || Successful || Successful || - || - | |||
|- | |||
| [[Item:Q88|1.4.E9]] || <math>f^{(n)} = f^{(n)}(x)</math> || <code>(f)^(n)= (f)^(n)*(x)</code> || <code>(f)^(n)= (f)^(n)*(x)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div> | |||
|- | |||
| [[Item:Q88|1.4.E9]] || <math>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</math> || <code>(f)^(n)*(x)= diff((f)^(n - 1)*(x), x)</code> || <code>(f)^(n)*(x)= D[(f)^(n - 1)*(x), x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div> | |||
|- | |||
| [[Item:Q95|1.4.E16]] || <math>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</math> || <code>int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x)</code> || <code>Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x]</code> || Successful || Successful || - || - | |||
|- | |- | ||
|} | |} | ||
Revision as of 00:43, 17 January 2020
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}} | binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k)) |
Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!] |
Successful | Successful | - | - |
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}} | (factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k) |
Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k] |
Successful | Successful | - | - |
| 1.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z}{k} = \frac{z(z-1)\cdots(z-k+1)}{k!}} | binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k)) |
Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!] |
Successful | Successful | - | - |
| 1.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}} | binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1) |
Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1] |
Successful | Successful | - | - |
| 1.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}} | sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m) |
Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m] |
Successful | Successful | - | - |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(2)}(x) = \deriv[2]{f}{x}} | (f)^(2)*(x)= diff(f, [x$(2)]) |
(f)^(2)*(x)= D[f, {x, 2}] |
Failure | Failure | Fail 0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1}0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2}0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3}0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1}0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2}0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3}0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1}0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2}0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3}0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1}0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2}0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)} | diff(f, [x$(2)])= diff(diff(f, x), x) |
D[f, {x, 2}]= D[D[f, x], x] |
Successful | Successful | - | - |
| 1.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)} = f^{(n)}(x)} | (f)^(n)= (f)^(n)*(x) |
(f)^(n)= (f)^(n)*(x) |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3} |
Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]} |
| 1.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)} | (f)^(n)*(x)= diff((f)^(n - 1)*(x), x) |
(f)^(n)*(x)= D[(f)^(n - 1)*(x), x] |
Failure | Failure | Fail .414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3} |
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]} |
| 1.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}} | int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x) |
Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x] |
Successful | Successful | - | - |