DLMF:17.6.E17 (Q5384)

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DLMF:17.6.E17
No description defined

    Statements

    Defining formula
    ϕ 1 2 ⁡ ( a , b c / q ; q , z ) - ϕ 1 2 ⁡ ( a , b c ; q , z ) = c ⁢ z ⁢ ( 1 - a ) ⁢ ( 1 - b ) ( q - c ) ⁢ ( 1 - c ) ⁢ ϕ 1 2 ⁡ ( a ⁢ q , b ⁢ q c ⁢ q ; q , z ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑞 𝑧 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 𝑐 𝑧 1 𝑎 1 𝑏 𝑞 𝑐 1 𝑐 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑞 𝑐 𝑞 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c/q};q,z\right)-{{% }_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=cz\frac{(1-a)(1-b)}{(q-c)(1-c)}{{}% _{2}\phi_{1}}\left({aq,bq\atop cq};q,z\right),}}
    0 references
    DLMF id
    DLMF:17.6.E17
    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.m2apdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1pdec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1jdec
    0 references
     
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