DLMF:17.9.E2 (Q5428)

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DLMF:17.9.E2
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    Statements

    test
    ϕ 1 2 ⁡ ( q - n , b c ; q , z ) = ( c / b ; q ) n ( c ; q ) n ⁢ b n ⁢ ϕ 1 3 ⁡ ( q - n , b , q / z b ⁢ q 1 - n / c ; q , z / c ) , q-hypergeometric-rphis 2 1 superscript 𝑞 𝑛 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑐 𝑏 𝑞 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑛 superscript 𝑏 𝑛 q-hypergeometric-rphis 3 1 superscript 𝑞 𝑛 𝑏 𝑞 𝑧 𝑏 superscript 𝑞 1 𝑛 𝑐 𝑞 𝑧 𝑐 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q^{-n},b\atop c};q,z\right)% =\frac{\left(c/b;q\right)_{n}}{\left(c;q\right)_{n}}b^{n}{{}_{3}\phi_{1}}\left% ({q^{-n},b,q/z\atop bq^{1-n}/c};q,z/c\right),}}
    0 references
    DLMF id
    DLMF:17.9.E2
    0 references
    Symbols used
    Q11298
    test
    ( 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.m2aadec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    test
    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.m2aadec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
    Q11711
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1dec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1adec
    0 references
     
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