DLMF:17.9.E11 (Q5437)

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DLMF:17.9.E11
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    Statements

    test
    ϕ 2 3 ⁡ ( q - n , b , c d , e ; q , q ) = ( e / c , d / c ; q ) n ( e , d ; q ) n ⁢ c n ⁢ ϕ 2 3 ⁡ ( q - n , c , c ⁢ b ⁢ q 1 - n / ( d ⁢ e ) c ⁢ q 1 - n / e , c ⁢ q 1 - n / d ; q , q ) , q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑏 𝑐 𝑑 𝑒 𝑞 𝑞 q-multiple-Pochhammer 𝑒 𝑐 𝑑 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑒 𝑑 𝑞 𝑛 superscript 𝑐 𝑛 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑐 𝑐 𝑏 superscript 𝑞 1 𝑛 𝑑 𝑒 𝑐 superscript 𝑞 1 𝑛 𝑒 𝑐 superscript 𝑞 1 𝑛 𝑑 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({q^{-n},b,c\atop d,e};q,q% \right)=\frac{\left(e/c,d/c;q\right)_{n}}{\left(e,d;q\right)_{n}}c^{n}{{}_{3}% \phi_{2}}\left({q^{-n},c,\ifrac{cbq^{1-n}}{(de)}\atop\ifrac{cq^{1-n}}{e},% \ifrac{cq^{1-n}}{d}};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E11
    0 references
    Symbols used
    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.m2ajdec
    0 references
    Q11713
    test
    ( 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.m6acdec
    0 references
     
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