DLMF:17.9.E3 (Q5429)

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DLMF:17.9.E3
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    test
    ϕ 1 2 ⁡ ( a , b c ; q , z ) = ( a ⁢ b ⁢ z / c ; q ) ∞ ( b ⁢ z / c ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( a , c / b , 0 c , c ⁢ q / ( b ⁢ z ) ; q , q ) + ( a , b ⁢ z , c / b ; q ) ∞ ( c , z , c / ( b ⁢ z ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( z , a ⁢ b ⁢ z / c , 0 b ⁢ z , b ⁢ z ⁢ q / c ; q , q ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-Pochhammer-symbol 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑎 𝑐 𝑏 0 𝑐 𝑐 𝑞 𝑏 𝑧 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑏 𝑧 𝑐 𝑏 𝑞 q-multiple-Pochhammer 𝑐 𝑧 𝑐 𝑏 𝑧 𝑞 q-hypergeometric-rphis 3 2 𝑧 𝑎 𝑏 𝑧 𝑐 0 𝑏 𝑧 𝑏 𝑧 𝑞 𝑐 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(abz/c;q\right)_{\infty}}{\left(bz/c;q\right)_{\infty}}{{}_{3}\phi_% {2}}\left({a,c/b,0\atop c,cq/(bz)};q,q\right)+\frac{\left(a,bz,c/b;q\right)_{% \infty}}{\left(c,z,c/(bz);q\right)_{\infty}}{{}_{3}\phi_{2}}\left({z,abz/c,0% \atop bz,bzq/c};q,q\right),}}
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    DLMF id
    DLMF:17.9.E3
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