Formula:6492

Digital Library of Mathematical Functions ID 18.18.E5

${\displaystyle{\displaystyle b_{n}=\frac{n!}{\Gamma\left(n+\alpha+1\right)}\int_{0}^{\infty}f(x)L^{(\alpha)}_{n}\left(x\right)e^{-x}x^{\alpha}\mathrm{d}x.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle f(z)}}$: analytic function
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.