DLMF:17.6.E24 (Q5391)

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DLMF:17.6.E24
No description defined

    Statements

    Defining formula
    ( 1 - c ) ⁢ ( q - c ) ⁢ ( a ⁢ b ⁢ z - c ) ⁢ ϕ 1 2 ⁡ ( a , b c / q ; q , z ) + z ⁢ ( c - a ) ⁢ ( c - b ) ⁢ ϕ 1 2 ⁡ ( a , b c ⁢ q ; q , z ) = ( c - 1 ) ⁢ ( c ⁢ ( q - c ) + z ⁢ ( c ⁢ a + c ⁢ b - a ⁢ b - a ⁢ b ⁢ q ) ) ⁢ ϕ 1 2 ⁡ ( a , b c ; q , z ) . 1 𝑐 𝑞 𝑐 𝑎 𝑏 𝑧 𝑐 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑞 𝑧 𝑧 𝑐 𝑎 𝑐 𝑏 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑞 𝑧 𝑐 1 𝑐 𝑞 𝑐 𝑧 𝑐 𝑎 𝑐 𝑏 𝑎 𝑏 𝑎 𝑏 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 {\displaystyle{\displaystyle(1-c)(q-c)(abz-c){{}_{2}\phi_{1}}\left({a,b\atop c% /q};q,z\right)+z(c-a)(c-b){{}_{2}\phi_{1}}\left({a,b\atop cq};q,z\right)=(c-1)% (c(q-c)+z(ca+cb-ab-abq)){{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right).}}
    0 references
    DLMF id
    DLMF:17.6.E24
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    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.m2awdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1wdec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1qdec
    0 references
     
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