DLMF:17.9.E8 (Q5434)

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DLMF:17.9.E8
No description defined

    Statements

    Defining formula
    ϕ 2 3 ⁡ ( q - n , b , c d , e ; q , q ) = ( d ⁢ e / ( b ⁢ c ) ; q ) n ( e ; q ) n ⁢ ( b ⁢ c d ) n ⁢ ϕ 2 3 ⁡ ( q - n , d / b , d / c d , d ⁢ e / ( b ⁢ c ) ; q , q ) , q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑏 𝑐 𝑑 𝑒 𝑞 𝑞 q-Pochhammer-symbol 𝑑 𝑒 𝑏 𝑐 𝑞 𝑛 q-Pochhammer-symbol 𝑒 𝑞 𝑛 superscript 𝑏 𝑐 𝑑 𝑛 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑑 𝑏 𝑑 𝑐 𝑑 𝑑 𝑒 𝑏 𝑐 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({q^{-n},b,c\atop d,e};q,q% \right)=\frac{\left(de/(bc);q\right)_{n}}{\left(e;q\right)_{n}}\left(\frac{bc}% {d}\right)^{n}{{}_{3}\phi_{2}}\left({q^{-n},d/b,d/c\atop d,de/(bc)};q,q\right)% ,}}
    0 references
    DLMF id
    DLMF:17.9.E8
    0 references
    Symbols used
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2aedec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2agdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1gdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1cdec
    0 references
     
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