DLMF:17.6.E13 (Q5380)

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DLMF:17.6.E13
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    Statements

    Defining formula
    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}},}}
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    DLMF id
    DLMF:17.6.E13
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