DLMF:17.4.E5 (Q5354): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11719 / rank
 
Normal rank
Property / Symbols used: Q11719 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11719 / qualifier
 
xml-id: C17.S1.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q11720 / rank
 
Normal rank
Property / Symbols used: Q11720 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11720 / qualifier
 
xml-id: C17.S1.XMD9.m1dec

Latest revision as of 14:55, 2 January 2020

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DLMF:17.4.E5
No description defined

    Statements

    Defining formula
    Φ ( 1 ) ⁡ ( a ; b , b ′ ; 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 + n , q-Appell-Phi-1 𝑎 𝑏 superscript 𝑏 ′ 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 𝑛 {\displaystyle{\displaystyle\Phi^{(1)}\left(a;b,b^{\prime};c;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+n}},}}
    0 references
    DLMF id
    DLMF:17.4.E5
    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.m2aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ddec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1dec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1bdec
    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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