Formula:6515

Digital Library of Mathematical Functions ID 18.18.E28

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)H_{n}\left(y\right)}{2^{n}n!}z^{n}=(1-z^{2})^{-\frac{1}{2}}\exp\left(\frac{2xyz-(x^{2}+y^{2})z^{2}}{1-z^{2}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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