Formula:6613

Digital Library of Mathematical Functions ID 18.25.E2

${\displaystyle{\displaystyle\int_{0}^{\infty}p_{n}(x)p_{m}(x)w(x)\mathrm{d}x=h_{n}\delta_{n,m}.}}$

Symbols List

• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle w(x)}}$: weight function
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle p_{n}(x)}}$: polynomial of degree n
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle h_{n}}}$: 18.2.E5
 

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