Formula:10185

Digital Library of Mathematical Functions ID 32.15.E1

${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\exp\left(-\tfrac{1}{4}\xi^{4}-z\xi^{2}\right)p_{m}(\xi)p_{n}(\xi)\mathrm{d}\xi=\delta_{m,n},}}$

Symbols List

• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: real
• ${\displaystyle{\displaystyle p_{n}(\xi)}}$: polynomials
 

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