DLMF:17.10.E1 (Q5447)

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DLMF:17.10.E1
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    Statements

    Defining formula
    ψ 2 2 ⁡ ( a , b c , d ; q , z ) = ( a ⁢ z , d / a , c / b , d ⁢ q / ( a ⁢ b ⁢ z ) ; q ) ∞ ( z , d , q / b , c ⁢ d / ( a ⁢ b ⁢ z ) ; q ) ∞ ⁢ ψ 2 2 ⁡ ( a , a ⁢ b ⁢ z / d a ⁢ z , c ; q , d a ) , q-hypergeometric-rpsis 2 2 𝑎 𝑏 𝑐 𝑑 𝑞 𝑧 q-multiple-Pochhammer 𝑎 𝑧 𝑑 𝑎 𝑐 𝑏 𝑑 𝑞 𝑎 𝑏 𝑧 𝑞 q-multiple-Pochhammer 𝑧 𝑑 𝑞 𝑏 𝑐 𝑑 𝑎 𝑏 𝑧 𝑞 q-hypergeometric-rpsis 2 2 𝑎 𝑎 𝑏 𝑧 𝑑 𝑎 𝑧 𝑐 𝑞 𝑑 𝑎 {\displaystyle{\displaystyle{{}_{2}\psi_{2}}\left({a,b\atop c,d};q,z\right)=% \frac{\left(az,d/a,c/b,dq/(abz);q\right)_{\infty}}{\left(z,d,q/b,cd/(abz);q% \right)_{\infty}}{{}_{2}\psi_{2}}\left({a,abz/d\atop az,c};q,\frac{d}{a}\right% ),}}
    0 references
    DLMF id
    DLMF:17.10.E1
    0 references
    Symbols used
    bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
    Defining formula
    ψ s r ⁡ ( a 1 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rpsis 𝑟 𝑠 subscript 𝑎 1 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E3.m2adec
    0 references
     
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