DLMF:17.6.E13 (Q5380)

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DLMF:17.6.E13
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    Statements

    test
    ϕ 1 2 ⁡ ( a , b ; c ; q , q ) + ( q / c , a , b ; q ) ∞ ( c / q , a ⁢ q / c , b ⁢ q / c ; q ) ∞ ⁢ ϕ 1 2 ⁡ ( a ⁢ q / c , b ⁢ q / c ; q 2 / c ; q , q ) = ( q / c , a ⁢ b ⁢ q / c ; q ) ∞ ( a ⁢ q / c , b ⁢ q / c ; q ) ∞ , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑞 q-multiple-Pochhammer 𝑞 𝑐 𝑎 𝑏 𝑞 q-multiple-Pochhammer 𝑐 𝑞 𝑎 𝑞 𝑐 𝑏 𝑞 𝑐 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑐 𝑏 𝑞 𝑐 superscript 𝑞 2 𝑐 𝑞 𝑞 q-multiple-Pochhammer 𝑞 𝑐 𝑎 𝑏 𝑞 𝑐 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑐 𝑏 𝑞 𝑐 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left(a,b;c;q,q\right)+\frac{\left% (q/c,a,b;q\right)_{\infty}}{\left(c/q,aq/c,bq/c;q\right)_{\infty}}{{}_{2}\phi_% {1}}\left(aq/c,bq/c;q^{2}/c;q,q\right)=\frac{\left(q/c,abq/c;q\right)_{\infty}% }{\left(aq/c,bq/c;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.6.E13
    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.m2aldec
    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.m6aidec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ldec
    0 references
     
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