Error Functions, Dawson’s and Fresnel Integrals - 7.10 Derivatives
Jump to navigation
Jump to search
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 7.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}}}
\deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(erf(z), [z$(n + 1)]) = (- 1)^(n)*(2)/(sqrt(Pi))*HermiteH(n, z)*exp(- (z)^(2))
|
D[Erf[z], {z, n + 1}] == (- 1)^(n)*Divide[2,Sqrt[Pi]]*HermiteH[n, z]*Exp[- (z)^(2)]
|
Failure | Failure | Manual Skip! | Failed [7 / 7]
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]]]}
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]]]}
... skip entries to safe data |
| 7.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z}}
\deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(Fresnelf(z), z) = - Pi*z*Fresnelg(z)
|
D[FresnelF[z], z] == - Pi*z*FresnelG[z]
|
Successful | Successful | - | Successful [Tested: 7] |
| 7.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1}
\deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(Fresnelg(z), z) = Pi*z*Fresnelf(z)- 1
|
D[FresnelG[z], z] == Pi*z*FresnelF[z]- 1
|
Successful | Successful | - | Successful [Tested: 7] |