DLMF:17.11.E3 (Q5455)

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DLMF:17.11.E3
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    Statements

    Defining formula
    Φ ( 3 ) ⁡ ( a , a ′ ; b , b ′ ; c ; q ; x , y ) = ( a , b ⁢ x ; q ) ∞ ( c , x ; q ) ∞ ⁢ ∑ n , r ≧ 0 ( a ′ , b ′ ; q ) n ⁢ ( x ; q ) r ⁢ ( c / a ; q ) n + r ⁢ a r ⁢ y n ( q , c / a ; q ) n ⁢ ( q , b ⁢ x ; q ) r . q-Appell-Phi-3 𝑎 superscript 𝑎 ′ 𝑏 superscript 𝑏 ′ 𝑐 𝑞 𝑥 𝑦 q-multiple-Pochhammer 𝑎 𝑏 𝑥 𝑞 q-multiple-Pochhammer 𝑐 𝑥 𝑞 subscript 𝑛 𝑟 0 q-multiple-Pochhammer superscript 𝑎 ′ superscript 𝑏 ′ 𝑞 𝑛 q-Pochhammer-symbol 𝑥 𝑞 𝑟 q-Pochhammer-symbol 𝑐 𝑎 𝑞 𝑛 𝑟 superscript 𝑎 𝑟 superscript 𝑦 𝑛 q-multiple-Pochhammer 𝑞 𝑐 𝑎 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑥 𝑞 𝑟 {\displaystyle{\displaystyle\Phi^{(3)}\left(a,a^{\prime};b,b^{\prime};c;q;x,y% \right)=\frac{\left(a,bx;q\right)_{\infty}}{\left(c,x;q\right)_{\infty}}\sum_{% n,r\geqq 0}\frac{\left(a^{\prime},b^{\prime};q\right)_{n}\left(x;q\right)_{r}% \left(c/a;q\right)_{n+r}a^{r}y^{n}}{\left(q,c/a;q\right)_{n}\left(q,bx;q\right% )_{r}}.}}
    0 references
    DLMF id
    DLMF:17.11.E3
    0 references
    Symbols used
    third $$q$$ -Appell function
    Defining formula
    Φ ( 3 ) ⁡ ( a , a ′ ; b , b ′ ; ; missing ; missing , missing ) q-Appell-Phi-3 𝑎 superscript 𝑎 ′ 𝑏 superscript 𝑏 ′ missing missing missing {\displaystyle{\displaystyle\Phi^{(3)}\left(\NVar{a},\NVar{a^{\prime}};\NVar{b% },\NVar{b^{\prime}};;missing;missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C17.S4.E7.m2adec
    0 references
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2aadec
    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.m6abdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1bdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1adec
    0 references
    Q11714
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C17.S1.XMD5.m1adec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1bdec
    0 references
    Q11720
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C17.S1.XMD9.m1bdec
    0 references
     
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