DLMF:17.6.E21 (Q5388)

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DLMF:17.6.E21
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    Statements

    test
    b ⁢ ( 1 - a ) ⁢ ϕ 1 2 ⁡ ( a ⁢ q , b c ; q , z ) - a ⁢ ( 1 - b ) ⁢ ϕ 1 2 ⁡ ( a , b ⁢ q c ; q , z ) = ( b - a ) ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) , 𝑏 1 𝑎 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑐 𝑞 𝑧 𝑎 1 𝑏 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑞 𝑐 𝑞 𝑧 𝑏 𝑎 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 {\displaystyle{\displaystyle b(1-a){{}_{2}\phi_{1}}\left({aq,b\atop c};q,z% \right)-a(1-b){{}_{2}\phi_{1}}\left({a,bq\atop c};q,z\right)=(b-a){{}_{2}\phi_% {1}}\left({a,b\atop c};q,z\right),}}
    0 references
    DLMF id
    DLMF:17.6.E21
    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.m2atdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1tdec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1ndec
    0 references
     
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