DLMF:17.11.E1 (Q5453)

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DLMF:17.11.E1
No description defined

    Statements

    Defining formula
    Φ ( 1 ) ⁡ ( a ; b , b ′ ; c ; q ; x , y ) = ( a , b ⁢ x , b ′ ⁢ y ; q ) ∞ ( c , x , y ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( c / a , x , y b ⁢ x , b ′ ⁢ y ; q , a ) , q-Appell-Phi-1 𝑎 𝑏 superscript 𝑏 ′ 𝑐 𝑞 𝑥 𝑦 q-multiple-Pochhammer 𝑎 𝑏 𝑥 superscript 𝑏 ′ 𝑦 𝑞 q-multiple-Pochhammer 𝑐 𝑥 𝑦 𝑞 q-hypergeometric-rphis 3 2 𝑐 𝑎 𝑥 𝑦 𝑏 𝑥 superscript 𝑏 ′ 𝑦 𝑞 𝑎 {\displaystyle{\displaystyle\Phi^{(1)}\left(a;b,b^{\prime};c;q;x,y\right)=% \frac{\left(a,bx,b^{\prime}y;q\right)_{\infty}}{\left(c,x,y;q\right)_{\infty}}% {{}_{3}\phi_{2}}\left({c/a,x,y\atop bx,b^{\prime}y};q,a\right),}}
    0 references
    DLMF id
    DLMF:17.11.E1
    0 references
    Symbols used
    first $$q$$ -Appell function
    Defining formula
    Φ ( 1 ) ⁡ ( a ; b , b ′ ; c ; q ; , missing ) q-Appell-Phi-1 𝑎 𝑏 superscript 𝑏 ′ 𝑐 𝑞 missing {\displaystyle{\displaystyle\Phi^{(1)}\left(\NVar{a};\NVar{b},\NVar{b^{\prime}% };\NVar{c};\NVar{q};,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C17.S4.E5.m2adec
    0 references
    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.m2adec
    0 references
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1dec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1dec
    0 references
    Q11720
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C17.S1.XMD9.m1dec
    0 references
     
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