View source for 7.10

{{DISPLAYTITLE:Error Functions, Dawson’s and Fresnel Integrals - 7.10 Derivatives}}

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! scope="col" style="position: sticky; top: 0;" | Formula 
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/7.10.E1 7.10.E1] || <math qid="Q2398">\deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(erf(z), [z$(n + 1)]) = (- 1)^(n)*(2)/(sqrt(Pi))*HermiteH(n, z)*exp(- (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Erf[z], {z, n + 1}] == (- 1)^(n)*Divide[2,Sqrt[Pi]]*HermiteH[n, z]*Exp[- (z)^(2)]</syntaxhighlight> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-3.565180358777125, 6.304771054937664], D[Complex[0.90211411820456, 0.25316491871645536]
Test Values: {Complex[0.8660254037844387, 0.49999999999999994], 4.0}]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[31.601340663516154, 7.3148164199817], D[Complex[-0.9777263798592635, 0.8570608779788039]
Test Values: {Complex[-0.4999999999999998, 0.8660254037844387], 4.0}]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/7.10#Ex1 7.10#Ex1] || <math qid="Q2401">\deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(Fresnelf(z), z) = - Pi*z*Fresnelg(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[FresnelF[z], z] == - Pi*z*FresnelG[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| [https://dlmf.nist.gov/7.10#Ex2 7.10#Ex2] || <math qid="Q2402">\deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(Fresnelg(z), z) = Pi*z*Fresnelf(z)- 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[FresnelG[z], z] == Pi*z*FresnelF[z]- 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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