DLMF:17.7.E21 (Q5417)

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DLMF:17.7.E21
No description defined

    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}},}}
    0 references
    DLMF id
    DLMF:17.7.E21
    0 references
    Symbols used
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6ardec
    0 references
    Q11715
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1tdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1idec
    0 references
     
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