DLMF:18.17.E36 (Q5777)

From testwiki
Revision as of 00:13, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.17.E36
No description defined

    Statements

    test
    ∫ - 1 1 ( 1 - x ) z - 1 ⁢ ( 1 + x ) β ⁢ P n ( α , β ) ⁡ ( x ) ⁢ d x = 2 β + z ⁢ Γ ⁡ ( z ) ⁢ Γ ⁡ ( 1 + β + n ) ⁢ ( 1 + α - z ) n n ! ⁢ Γ ⁡ ( 1 + β + z + n ) , superscript subscript 1 1 superscript 1 𝑥 𝑧 1 superscript 1 𝑥 𝛽 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑥 superscript 2 𝛽 𝑧 Euler-Gamma 𝑧 Euler-Gamma 1 𝛽 𝑛 Pochhammer 1 𝛼 𝑧 𝑛 𝑛 Euler-Gamma 1 𝛽 𝑧 𝑛 {\displaystyle{\displaystyle\int_{-1}^{1}(1-x)^{z-1}(1+x)^{\beta}P^{(\alpha,% \beta)}_{n}\left(x\right)\mathrm{d}x=\frac{2^{\beta+z}\Gamma\left(z\right)% \Gamma\left(1+\beta+n\right){\left(1+\alpha-z\right)_{n}}}{n!\Gamma\left(1+% \beta+z+n\right)},}}
    0 references
    DLMF id
    DLMF:18.17.E36
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2andec
    0 references
    Q11660
    test
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2afdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5777&oldid=33193"