DLMF:17.4.E8 (Q5357)

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DLMF:17.4.E8
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    Statements

    Defining formula
    Φ ( 4 ) ⁡ ( a , b ; c , c ′ ; q ; x , y ) = ∑ m , n ≥ 0 ( a , b ; q ) m + n ⁢ x m ⁢ y n ( q , c ; q ) m ⁢ ( q , c ′ ; q ) n . q-Appell-Phi-4 𝑎 𝑏 𝑐 superscript 𝑐 ′ 𝑞 𝑥 𝑦 subscript 𝑚 𝑛 0 q-Pochhammer-symbol 𝑎 𝑏 𝑞 𝑚 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 q-multiple-Pochhammer 𝑞 𝑐 𝑞 𝑚 q-multiple-Pochhammer 𝑞 superscript 𝑐 ′ 𝑞 𝑛 {\displaystyle{\displaystyle\Phi^{(4)}\left(a,b;c,c^{\prime};q;x,y\right)=\sum% _{m,n\geq 0}\frac{\left(a,b;q\right)_{m+n}x^{m}y^{n}}{\left(q,c;q\right)_{m}% \left(q,c^{\prime};q\right)_{n}}.}}
    0 references
    DLMF id
    DLMF:17.4.E8
    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.m2addec
    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.m1gdec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1cdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1edec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1cdec
    0 references
     
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