DLMF:18.10.E9 (Q5633): Difference between revisions

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Property / constraint
 

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

\alpha>-1
Property / constraint: α > - 1 𝛼 1 {\displaystyle{\displaystyle\alpha>-1}} / rank
 
Normal rank

Revision as of 16:59, 30 December 2019

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DLMF:18.10.E9
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    Statements

    L n ( α ) ( x ) = e x x - 1 2 α n ! 0 e - t t n + 1 2 α J α ( 2 x t ) d t , Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript 𝑒 𝑥 superscript 𝑥 1 2 𝛼 𝑛 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝑛 1 2 𝛼 Bessel-J 𝛼 2 𝑥 𝑡 𝑡 {\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,}}
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    α > - 1 𝛼 1 {\displaystyle{\displaystyle\alpha>-1}}
    0 references