DLMF:17.11.E2 (Q5454)

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DLMF:17.11.E2
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    Statements

    Defining formula
    Φ ( 2 ) ⁡ ( a ; b , b ′ ; c , c ′ ; q ; x , y ) = ( b , a ⁢ x ; q ) ∞ ( c , x ; q ) ∞ ⁢ ∑ n , r ≧ 0 ( a , b ′ ; q ) n ⁢ ( c / b , x ; q ) r ⁢ b r ⁢ y n ( q , c ′ ; q ) n ⁢ ( q ) r ⁢ ( a ⁢ x ; q ) n + r , q-Appell-Phi-2 𝑎 𝑏 superscript 𝑏 ′ 𝑐 superscript 𝑐 ′ 𝑞 𝑥 𝑦 q-multiple-Pochhammer 𝑏 𝑎 𝑥 𝑞 q-multiple-Pochhammer 𝑐 𝑥 𝑞 subscript 𝑛 𝑟 0 q-multiple-Pochhammer 𝑎 superscript 𝑏 ′ 𝑞 𝑛 q-multiple-Pochhammer 𝑐 𝑏 𝑥 𝑞 𝑟 superscript 𝑏 𝑟 superscript 𝑦 𝑛 q-multiple-Pochhammer 𝑞 superscript 𝑐 ′ 𝑞 𝑛 Pochhammer 𝑞 𝑟 q-Pochhammer-symbol 𝑎 𝑥 𝑞 𝑛 𝑟 {\displaystyle{\displaystyle\Phi^{(2)}\left(a;b,b^{\prime};c,c^{\prime};q;x,y% \right)=\frac{\left(b,ax;q\right)_{\infty}}{\left(c,x;q\right)_{\infty}}\sum_{% n,r\geqq 0}\frac{\left(a,b^{\prime};q\right)_{n}\left(c/b,x;q\right)_{r}b^{r}y% ^{n}}{\left(q,c^{\prime};q\right)_{n}{\left(q\right)_{r}}\left(ax;q\right)_{n+% r}},}}
    0 references
    DLMF id
    DLMF:17.11.E2
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    second $$q$$ -Appell function
    Defining formula
    Φ ( 2 ) ⁡ ( a ; b , b ′ ; c , c ⁢ missing ⁢ missing ⁢ missing ; missing ; missing , missing ) q-Appell-Phi-2 𝑎 𝑏 superscript 𝑏 ′ 𝑐 𝑐 missing missing missing missing missing missing {\displaystyle{\displaystyle\Phi^{(2)}\left(\NVar{a};\NVar{b},\NVar{b^{\prime}% };\NVar{c},\NVar{c}{missing}{missing}{missing};missing;missing,missing\right)% \)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C17.S4.E6.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.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.m6aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
     
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