Formula:6355

Digital Library of Mathematical Functions ID 18.12.E16

${\displaystyle{\displaystyle e^{xz-\frac{1}{2}z^{2}}=\sum_{n=0}^{\infty}\frac{\mathit{He}_{n}\left(x\right)}{n!}z^{n}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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