DLMF:18.17.E15 (Q5756): Difference between revisions

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Property / constraint
 

μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}

\mu>0
Property / constraint: μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}} / rank
 
Normal rank

Revision as of 17:01, 30 December 2019

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DLMF:18.17.E15
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    e - x L n ( α ) ( x ) = x e - y L n ( α + μ ) ( y ) ( y - x ) μ - 1 Γ ( μ ) d y , superscript 𝑒 𝑥 Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript subscript 𝑥 superscript 𝑒 𝑦 Laguerre-polynomial-L 𝛼 𝜇 𝑛 𝑦 superscript 𝑦 𝑥 𝜇 1 Euler-Gamma 𝜇 𝑦 {\displaystyle{\displaystyle e^{-x}L^{(\alpha)}_{n}\left(x\right)=\int_{x}^{% \infty}e^{-y}L^{(\alpha+\mu)}_{n}\left(y\right)\frac{(y-x)^{\mu-1}}{\Gamma% \left(\mu\right)}\mathrm{d}y,}}
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    μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}
    0 references