DLMF:17.6.E22 (Q5389)

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DLMF:17.6.E22
No description defined

    Statements

    test
    a ⁢ ( 1 - b c ) ⁢ ϕ 1 2 ⁡ ( a , b / q c ; q , z ) - b ⁢ ( 1 - a c ) ⁢ ϕ 1 2 ⁡ ( a / q , b c ; q , z ) = ( a - b ) ⁢ ( 1 - a ⁢ b ⁢ z c ⁢ q ) ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) , 𝑎 1 𝑏 𝑐 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑞 𝑐 𝑞 𝑧 𝑏 1 𝑎 𝑐 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑐 𝑞 𝑧 𝑎 𝑏 1 𝑎 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 {\displaystyle{\displaystyle a\left(1-\frac{b}{c}\right){{}_{2}\phi_{1}}\left(% {a,b/q\atop c};q,z\right)-b\left(1-\frac{a}{c}\right){{}_{2}\phi_{1}}\left({a/% q,b\atop c};q,z\right)=(a-b)\left(1-\frac{abz}{cq}\right){{}_{2}\phi_{1}}\left% ({a,b\atop c};q,z\right),}}
    0 references
    DLMF id
    DLMF:17.6.E22
    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.m2audec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1udec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1odec
    0 references
     
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