DLMF:31.11.E12 (Q9098)

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DLMF:31.11.E12
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    Statements

    Defining formula
    P j = Γ ⁡ ( α + j ) ⁢ Γ ⁡ ( 1 - γ + α + j ) Γ ⁡ ( 1 + α - β + ϵ + 2 ⁢ j ) ⁢ z - α - j ⁢ F 1 2 ⁡ ( α + j , 1 - γ + α + j 1 + α - β + ϵ + 2 ⁢ j ; 1 z ) , subscript 𝑃 𝑗 Euler-Gamma 𝛼 𝑗 Euler-Gamma 1 𝛾 𝛼 𝑗 Euler-Gamma 1 𝛼 𝛽 italic-ϵ 2 𝑗 superscript 𝑧 𝛼 𝑗 Gauss-hypergeometric-F-as-2F1 𝛼 𝑗 1 𝛾 𝛼 𝑗 1 𝛼 𝛽 italic-ϵ 2 𝑗 1 𝑧 {\displaystyle{\displaystyle P_{j}=\frac{\Gamma\left(\alpha+j\right)\Gamma% \left(1-\gamma+\alpha+j\right)}{\Gamma\left(1+\alpha-\beta+\epsilon+2j\right)}% z^{-\alpha-j}\*{{}_{2}F_{1}}\left({\alpha+j,1-\gamma+\alpha+j\atop 1+\alpha-% \beta+\epsilon+2j};\frac{1}{z}\right),}}
    0 references
    DLMF id
    DLMF:31.11.E12
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5adec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1bdec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1edec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1cdec
    0 references
    Q12477
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C31.S1.XMD2.m1fdec
    0 references
     
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