DLMF:17.4.E6 (Q5355)

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DLMF:17.4.E6
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    Statements

    Defining formula
    Φ ( 2 ) ⁡ ( a ; b , b ′ ; c , c ′ ; q ; x , y ) = ∑ m , n ≥ 0 ( a ; q ) m + n ⁢ ( b ; q ) m ⁢ ( b ′ ; q ) n ⁢ x m ⁢ y n ( q ; q ) m ⁢ ( q ; q ) n ⁢ ( c ; q ) m ⁢ ( c ′ ; q ) n , q-Appell-Phi-2 𝑎 𝑏 superscript 𝑏 ′ 𝑐 superscript 𝑐 ′ 𝑞 𝑥 𝑦 subscript 𝑚 𝑛 0 q-Pochhammer-symbol 𝑎 𝑞 𝑚 𝑛 q-Pochhammer-symbol 𝑏 𝑞 𝑚 q-Pochhammer-symbol superscript 𝑏 ′ 𝑞 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑚 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑚 q-Pochhammer-symbol superscript 𝑐 ′ 𝑞 𝑛 {\displaystyle{\displaystyle\Phi^{(2)}\left(a;b,b^{\prime};c,c^{\prime};q;x,y% \right)=\sum_{m,n\geq 0}\frac{\left(a;q\right)_{m+n}\left(b;q\right)_{m}\left(% b^{\prime};q\right)_{n}x^{m}y^{n}}{\left(q;q\right)_{m}\left(q;q\right)_{n}% \left(c;q\right)_{m}\left(c^{\prime};q\right)_{n}},}}
    0 references
    DLMF id
    DLMF:17.4.E6
    0 references
    Symbols used
    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.m2abdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1edec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1adec
    0 references
     
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