Formula:6494

Digital Library of Mathematical Functions ID 18.18.E7

${\displaystyle{\displaystyle d_{n}=\frac{1}{\sqrt{\pi}2^{n}n!}\int_{-\infty}^{\infty}f(x)H_{n}\left(x\right)e^{-x^{2}}\mathrm{d}x.}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle f(z)}}$: analytic function
• ${\displaystyle{\displaystyle x}}$: real variable
 

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