DLMF:18.17.E11 (Q5752): Difference between revisions

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Property / constraint
 

x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}}

x>1
Property / constraint: x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}} / rank
 
Normal rank

Revision as of 17:01, 30 December 2019

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DLMF:18.17.E11
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    Statements

    test
    Γ ⁡ ( n + α + β - μ + 1 ) x n + α + β - μ + 1 ⁢ P n ( α , β - μ ) ⁡ ( 1 - 2 ⁢ x - 1 ) = ∫ x ∞ Γ ⁡ ( n + α + β + 1 ) y n + α + β + 1 ⁢ P n ( α , β ) ⁡ ( 1 - 2 ⁢ y - 1 ) ⁢ ( y - x ) μ - 1 Γ ⁡ ( μ ) ⁢ d y , Euler-Gamma 𝑛 𝛼 𝛽 𝜇 1 superscript 𝑥 𝑛 𝛼 𝛽 𝜇 1 Jacobi-polynomial-P 𝛼 𝛽 𝜇 𝑛 1 2 superscript 𝑥 1 superscript subscript 𝑥 Euler-Gamma 𝑛 𝛼 𝛽 1 superscript 𝑦 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 2 superscript 𝑦 1 superscript 𝑦 𝑥 𝜇 1 Euler-Gamma 𝜇 𝑦 {\displaystyle{\displaystyle\frac{\Gamma\left(n+\alpha+\beta-\mu+1\right)}{x^{% n+\alpha+\beta-\mu+1}}P^{(\alpha,\beta-\mu)}_{n}\left(1-2x^{-1}\right)=\int_{x% }^{\infty}\frac{\Gamma\left(n+\alpha+\beta+1\right)}{y^{n+\alpha+\beta+1}}P^{(% \alpha,\beta)}_{n}\left(1-2y^{-1}\right)\*\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu% \right)}\mathrm{d}y,}}
    0 references
    DLMF id
    DLMF:18.17.E11
    0 references
    constraint
    x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}}
    0 references
     
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