Formula:6482

Digital Library of Mathematical Functions ID 18.17.E44

${\displaystyle{\displaystyle\int_{-1}^{1}\frac{P_{n}\left(x\right)-P_{n}\left(t\right)}{|x-t|}\mathrm{d}t=2\left(1+\tfrac{1}{2}+\dots+\tfrac{1}{n}\right)P_{n}\left(x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-1\leq x\leq 1}}$

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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