Formula:3156

Digital Library of Mathematical Functions ID 7.18.E8

${\displaystyle{\displaystyle(-1)^{n}\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)+\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(-z\right)=\frac{i^{-n}}{2^{n-1}n!}H_{n}\left(iz\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(\NVar{z}\right)}}$: repeated integrals of the complementary error function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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