Error Functions, Dawson’s and Fresnel Integrals - 7.10 Derivatives

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
7.10.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n+1}\operatorname{erf}z}{{\mathrm{d}z}^{n+1}}=(-1)^{n}\frac{2}{\sqrt{\pi}}H_{n}\left(z\right)e^{-z^{2}}}}$ \deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}}		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	${\displaystyle{\displaystyle\frac{\mathrm{d}\mathrm{f}\left(z\right)}{\mathrm{d}z}=-\pi z\mathrm{g}\left(z\right)}}$ \deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z}		diff(Fresnelf(z), z) = - Pi*z*Fresnelg(z)	D[FresnelF[z], z] == - Pi*z*FresnelG[z]	Successful	Successful	-	Successful [Tested: 7]
7.10#Ex2	${\displaystyle{\displaystyle\frac{\mathrm{d}\mathrm{g}\left(z\right)}{\mathrm{d}z}=\pi z\mathrm{f}\left(z\right)-1}}$ \deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1		diff(Fresnelg(z), z) = Pi*z*Fresnelf(z)- 1	D[FresnelG[z], z] == Pi*z*FresnelF[z]- 1	Successful	Successful	-	Successful [Tested: 7]