Gold 11
Error function
- Gold ID
- 11
- Link
- https://sigir21.wmflabs.org/wiki/Error_function#math.61.27
- Formula
- TeX Source
\operatorname{erf}^{(k)}(z) = \frac{2 (-1)^{k-1}}{\sqrt{\pi}} \mathit{H}_{k-1}(z) e^{-z^2} = \frac{2}{\sqrt{\pi}} \frac{d^{k-1}}{dz^{k-1}} \left(e^{-z^2}\right),\qquad k=1, 2, \dots
| Translation Results | ||
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| Semantic LaTeX | Mathematica Translation | Maple Translations |
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Semantic LaTeX
- Translation
\erf@@{(z)}^{(k)} = \frac{2 (-1)^{k-1}}{\sqrt{\cpi}} \HermitepolyH{k-1}@{z} \expe^{-z^2} = \frac{2}{\sqrt{\cpi}} \deriv [{k-1}]{ }{z}(\expe^{-z^2}) , \qquad k = 1 , 2 , \dots- Expected (Gold Entry)
\erf@@{(z)}^{(k)} = \frac{2 (-1)^{k-1}}{\sqrt{\cpi}} \HermitepolyH{k-1}@{z} \expe^{-z^2} = \frac{2}{\sqrt{\cpi}} \deriv [{k-1}]{ }{z}(\expe^{-z^2}) , \qquad k = 1 , 2 , \dots
Mathematica
- Translation
(Erf[z])^(k) == Divide[2*(- 1)^(k - 1),Sqrt[Pi]]*HermiteH[k - 1, z]*Exp[- (z)^(2)] == Divide[2,Sqrt[Pi]]*(D[(Exp[- (temp)^(2)]), {temp, k - 1}]/.temp-> z)- Expected (Gold Entry)
D[Erf[z], {z, k}] == Divide[2*(- 1)^(k - 1),Sqrt[Pi]]*HermiteH[k - 1, z]*Exp[- (z)^(2)] == Divide[2,Sqrt[Pi]]*D[Exp[- (z)^(2)], {z, k - 1}]
Maple
- Translation
(erf(z))^(k) = (2*(- 1)^(k - 1))/(sqrt(Pi))*HermiteH(k - 1, z)*exp(- (z)^(2)) = (2)/(sqrt(Pi))*subs( temp=z, diff( (exp(- (temp)^(2))), temp$(k - 1) ) )- Expected (Gold Entry)
diff(erf(z), [z$\$$k]) = (2*(- 1)^(k - 1))/(sqrt(Pi))*HermiteH(k - 1, z)*exp(- (z)^(2)) = (2)/(sqrt(Pi))*diff(exp(- (z)^(2)), [z$\$$(k - 1)])