DLMF:17.7.E21 (Q5417)

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DLMF:17.7.E21
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    Statements

    Defining formula
    ∑ k = 0 n ( 1 - a ⁢ p k ⁢ q k ) ⁢ ( 1 - b ⁢ p k ⁢ q - k ) ( 1 - a ) ⁢ ( 1 - b ) ⁢ ( a , b ; p ) k ⁢ ( c , a / ( b ⁢ c ) ; q ) k ( q , a ⁢ q / b ; q ) k ⁢ ( a ⁢ p / c , b ⁢ c ⁢ p ; p ) k ⁢ q k = ( a ⁢ p , b ⁢ p ; p ) n ⁢ ( c ⁢ q , a ⁢ q / ( b ⁢ c ) ; q ) n ( q , a ⁢ q / b ; q ) n ⁢ ( a ⁢ p / c , b ⁢ c ⁢ p ; p ) n , superscript subscript 𝑘 0 𝑛 1 𝑎 superscript 𝑝 𝑘 superscript 𝑞 𝑘 1 𝑏 superscript 𝑝 𝑘 superscript 𝑞 𝑘 1 𝑎 1 𝑏 q-multiple-Pochhammer 𝑎 𝑏 𝑝 𝑘 q-multiple-Pochhammer 𝑐 𝑎 𝑏 𝑐 𝑞 𝑘 q-multiple-Pochhammer 𝑞 𝑎 𝑞 𝑏 𝑞 𝑘 q-multiple-Pochhammer 𝑎 𝑝 𝑐 𝑏 𝑐 𝑝 𝑝 𝑘 superscript 𝑞 𝑘 q-multiple-Pochhammer 𝑎 𝑝 𝑏 𝑝 𝑝 𝑛 q-multiple-Pochhammer 𝑐 𝑞 𝑎 𝑞 𝑏 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑎 𝑞 𝑏 𝑞 𝑛 q-multiple-Pochhammer 𝑎 𝑝 𝑐 𝑏 𝑐 𝑝 𝑝 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n}\frac{(1-ap^{k}q^{k})(1-bp^{k}q^{-k}% )}{(1-a)(1-b)}\frac{\left(a,b;p\right)_{k}\left(c,a/(bc);q\right)_{k}}{\left(q% ,aq/b;q\right)_{k}\left(ap/c,bcp;p\right)_{k}}q^{k}=\frac{\left(ap,bp;p\right)% _{n}\left(cq,aq/(bc);q\right)_{n}}{\left(q,aq/b;q\right)_{n}\left(ap/c,bcp;p% \right)_{n}},}}
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    DLMF id
    DLMF:17.7.E21
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