DLMF:17.4.E1 (Q5350)

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DLMF:17.4.E1
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    Statements

    Defining formula
    ϕ s r + 1 ⁡ ( a 0 , a 1 , a 2 , … , a r b 1 , b 2 , … , b s ; q , z ) = ϕ s r + 1 ⁡ ( a 0 , a 1 , … , a r ; b 1 , b 2 , … , b s ; q , z ) = ∑ n = 0 ∞ ( a 0 ; q ) n ⁢ ( a 1 ; q ) n ⁢ ⋯ ⁢ ( a r ; q ) n ( q ; q ) n ⁢ ( b 1 ; q ) n ⁢ ⋯ ⁢ ( b s ; q ) n ⁢ ( ( - 1 ) n ⁢ q ( n 2 ) ) s - r ⁢ z n . q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 subscript 𝑏 1 subscript 𝑏 2 … subscript 𝑏 𝑠 𝑞 𝑧 q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 subscript 𝑎 1 … subscript 𝑎 𝑟 subscript 𝑏 1 subscript 𝑏 2 … subscript 𝑏 𝑠 𝑞 𝑧 superscript subscript 𝑛 0 q-Pochhammer-symbol subscript 𝑎 0 𝑞 𝑛 q-Pochhammer-symbol subscript 𝑎 1 𝑞 𝑛 ⋯ q-Pochhammer-symbol subscript 𝑎 𝑟 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol subscript 𝑏 1 𝑞 𝑛 ⋯ q-Pochhammer-symbol subscript 𝑏 𝑠 𝑞 𝑛 superscript superscript 1 𝑛 superscript 𝑞 binomial 𝑛 2 𝑠 𝑟 superscript 𝑧 𝑛 {\displaystyle{\displaystyle{{}_{r+1}\phi_{s}}\left({a_{0},a_{1},a_{2},\dots,a% _{r}\atop b_{1},b_{2},\dots,b_{s}};q,z\right)={{}_{r+1}\phi_{s}}\left(a_{0},a_% {1},\dots,a_{r};b_{1},b_{2},\dots,b_{s};q,z\right)=\sum_{n=0}^{\infty}\frac{% \left(a_{0};q\right)_{n}\left(a_{1};q\right)_{n}\cdots\left(a_{r};q\right)_{n}% }{\left(q;q\right)_{n}\left(b_{1};q\right)_{n}\cdots\left(b_{s};q\right)_{n}}% \*\left((-1)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}\right)^{s-r}z^{n}.}}
    0 references
    DLMF id
    DLMF:17.4.E1
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
     
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