Formula:6328

Digital Library of Mathematical Functions ID 18.10.E7

${\displaystyle{\displaystyle H_{n}\left(x\right)=\frac{2^{n}}{\pi^{\frac{1}{2}}}\int_{-\infty}^{\infty}(x+it)^{n}e^{-t^{2}}\mathrm{d}t.}}$

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
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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