DLMF:17.6.E19 (Q5386)

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DLMF:17.6.E19
No description defined

    Statements

    Defining formula
    ϕ 1 2 ⁡ ( a ⁢ q , b c ⁢ q ; q , z ) - ϕ 1 2 ⁡ ( a , b c ; q , z ) = a ⁢ z ⁢ ( 1 - b ) ⁢ ( 1 - ( c / a ) ) ( 1 - c ) ⁢ ( 1 - c ⁢ q ) ⁢ ϕ 1 2 ⁡ ( a ⁢ q , b ⁢ q c ⁢ q 2 ; q , z ) , q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑐 𝑞 𝑞 𝑧 q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 𝑎 𝑧 1 𝑏 1 𝑐 𝑎 1 𝑐 1 𝑐 𝑞 q-hypergeometric-rphis 2 1 𝑎 𝑞 𝑏 𝑞 𝑐 superscript 𝑞 2 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({aq,b\atop cq};q,z\right)-{{% }_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=az\frac{(1-b)(1-(c/a))}{(1-c)(1-cq% )}{{}_{2}\phi_{1}}\left({aq,bq\atop cq^{2}};q,z\right),}}
    0 references
    DLMF id
    DLMF:17.6.E19
    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.m2ardec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1rdec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1ldec
    0 references
     
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