Formula:6440

Digital Library of Mathematical Functions ID 18.17.E2

${\displaystyle{\displaystyle\int_{0}^{x}L_{m}\left(y\right)L_{n}\left(x-y\right)\mathrm{d}y=\int_{0}^{x}L_{m+n}\left(y\right)\mathrm{d}y=L_{m+n}\left(x\right)-L_{m+n+1}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle L_{\NVar{n}}\left(\NVar{x}\right)=L^{(0)}_{n}\left(x\right)}}$: Laguerre polynomial
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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