DLMF:18.17.E14 (Q5755): Difference between revisions

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Property / constraint
 

x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}

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

Revision as of 17:01, 30 December 2019

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DLMF:18.17.E14
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    Statements

    test
    x α + μ ⁢ L n ( α + μ ) ⁡ ( x ) Γ ⁡ ( α + μ + n + 1 ) = ∫ 0 x y α ⁢ L n ( α ) ⁡ ( y ) Γ ⁡ ( α + n + 1 ) ⁢ ( x - y ) μ - 1 Γ ⁡ ( μ ) ⁢ d y , superscript 𝑥 𝛼 𝜇 Laguerre-polynomial-L 𝛼 𝜇 𝑛 𝑥 Euler-Gamma 𝛼 𝜇 𝑛 1 superscript subscript 0 𝑥 superscript 𝑦 𝛼 Laguerre-polynomial-L 𝛼 𝑛 𝑦 Euler-Gamma 𝛼 𝑛 1 superscript 𝑥 𝑦 𝜇 1 Euler-Gamma 𝜇 𝑦 {\displaystyle{\displaystyle\frac{x^{\alpha+\mu}L^{(\alpha+\mu)}_{n}\left(x% \right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{0}^{x}\frac{y^{\alpha}L^{(% \alpha)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}\frac{(x-y)^{\mu-1}}% {\Gamma\left(\mu\right)}\mathrm{d}y,}}
    0 references
    DLMF id
    DLMF:18.17.E14
    0 references
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
     
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