DLMF:19.19.E3 (Q6363)

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DLMF:19.19.E3
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    Statements

    Defining formula
    R - a ⁡ ( 𝐛 ; 𝐳 ) = z n - a ⁢ ∑ N = 0 ∞ ( a ) N ( c ) N ⁢ T N ⁢ ( b 1 , … , b n - 1 ; 1 - ( z 1 / z n ) , … , 1 - ( z n - 1 / z n ) ) , Carlson-integral-R 𝑎 𝐛 𝐳 superscript subscript 𝑧 𝑛 𝑎 superscript subscript 𝑁 0 Pochhammer 𝑎 𝑁 Pochhammer 𝑐 𝑁 subscript 𝑇 𝑁 subscript 𝑏 1 … subscript 𝑏 𝑛 1 1 subscript 𝑧 1 subscript 𝑧 𝑛 … 1 subscript 𝑧 𝑛 1 subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=z_{n}^{-% a}\sum_{N=0}^{\infty}\frac{{\left(a\right)_{N}}}{{\left(c\right)_{N}}}\*{T_{N}% (b_{1},\dots,b_{n-1};1-(z_{1}/z_{n}),\dots,1-(z_{n-1}/z_{n}))},}}
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    DLMF id
    DLMF:19.19.E3
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    constraint
    | 1 - ( z j / z n ) | < 1 1 subscript 𝑧 𝑗 subscript 𝑧 𝑛 1 {\displaystyle{\displaystyle|1-(z_{j}/z_{n})|<1}}
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    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2aadec
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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
     
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