DLMF:18.10.E9

MaRDI QIDQ6330

• Label: DLMF:18.10.E9

Digital Library of Mathematical Functions ID 18.10.E9

${\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\frac{e^{x}x^{-\frac{1}{2}\alpha}}{n!}\int_{0}^{\infty}e^{-t}t^{n+\frac{1}{2}\alpha}J_{\alpha}\left(2\sqrt{xt}\right)\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\alpha>-1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: 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
• ${\displaystyle{\displaystyle x}}$: real variable
 

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