DLMF:17.6.E27 (Q5394)

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DLMF:17.6.E27
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    z ⁢ ( c - a ⁢ b ⁢ q ⁢ z ) ⁢ 𝒟 q 2 ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) + ( 1 - c 1 - q + ( 1 - a ) ⁢ ( 1 - b ) - ( 1 - a ⁢ b ⁢ q ) 1 - q ⁢ z ) ⁢ 𝒟 q ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) - ( 1 - a ) ⁢ ( 1 - b ) ( 1 - q ) 2 ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) = 0 . 𝑧 𝑐 𝑎 𝑏 𝑞 𝑧 superscript subscript 𝒟 𝑞 2 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 1 𝑐 1 𝑞 1 𝑎 1 𝑏 1 𝑎 𝑏 𝑞 1 𝑞 𝑧 subscript 𝒟 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 1 𝑎 1 𝑏 superscript 1 𝑞 2 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 0 {\displaystyle{\displaystyle z(c-abqz)\mathcal{D}_{q}^{2}{{}_{2}\phi_{1}}\left% ({a,b\atop c};q,z\right)+\left(\frac{1-c}{1-q}+\frac{(1-a)(1-b)-(1-abq)}{1-q}z% \right)\mathcal{D}_{q}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)-\frac{(1-a% )(1-b)}{(1-q)^{2}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=0.}}
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    DLMF:17.6.E27
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