DLMF:17.9.E19 (Q5445): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11711 / rank
 
Normal rank
Property / Symbols used: Q11711 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1idec

Revision as of 15:07, 2 January 2020

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DLMF:17.9.E19
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    Statements

    Defining formula
    ∑ n = 0 ∞ ( a ; q 2 ) n ⁢ ( b ; q ) n ( q 2 ; q 2 ) n ⁢ ( c ; q ) n ⁢ z n = ( b ; q ) ∞ ⁢ ( a ⁢ z ; q 2 ) ∞ ( c ; q ) ∞ ⁢ ( z ; q 2 ) ∞ ⁢ ∑ n = 0 ∞ ( c / b ; q ) 2 ⁢ n ⁢ ( z ; q 2 ) n ⁢ b 2 ⁢ n ( q ; q ) 2 ⁢ n ⁢ ( a ⁢ z ; q 2 ) n + ( b ; q ) ∞ ⁢ ( a ⁢ z ⁢ q ; q 2 ) ∞ ( c ; q ) ∞ ⁢ ( z ⁢ q ; q 2 ) ∞ ⁢ ∑ n = 0 ∞ ( c / b ; q ) 2 ⁢ n + 1 ⁢ ( z ⁢ q ; q 2 ) n ⁢ b 2 ⁢ n + 1 ( q ; q ) 2 ⁢ n + 1 ⁢ ( a ⁢ z ⁢ q ; q 2 ) n . superscript subscript 𝑛 0 q-Pochhammer-symbol 𝑎 superscript 𝑞 2 𝑛 q-Pochhammer-symbol 𝑏 𝑞 𝑛 q-Pochhammer-symbol superscript 𝑞 2 superscript 𝑞 2 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑛 superscript 𝑧 𝑛 q-Pochhammer-symbol 𝑏 𝑞 q-Pochhammer-symbol 𝑎 𝑧 superscript 𝑞 2 q-Pochhammer-symbol 𝑐 𝑞 q-Pochhammer-symbol 𝑧 superscript 𝑞 2 superscript subscript 𝑛 0 q-Pochhammer-symbol 𝑐 𝑏 𝑞 2 𝑛 q-Pochhammer-symbol 𝑧 superscript 𝑞 2 𝑛 superscript 𝑏 2 𝑛 q-Pochhammer-symbol 𝑞 𝑞 2 𝑛 q-Pochhammer-symbol 𝑎 𝑧 superscript 𝑞 2 𝑛 q-Pochhammer-symbol 𝑏 𝑞 q-Pochhammer-symbol 𝑎 𝑧 𝑞 superscript 𝑞 2 q-Pochhammer-symbol 𝑐 𝑞 q-Pochhammer-symbol 𝑧 𝑞 superscript 𝑞 2 superscript subscript 𝑛 0 q-Pochhammer-symbol 𝑐 𝑏 𝑞 2 𝑛 1 q-Pochhammer-symbol 𝑧 𝑞 superscript 𝑞 2 𝑛 superscript 𝑏 2 𝑛 1 q-Pochhammer-symbol 𝑞 𝑞 2 𝑛 1 q-Pochhammer-symbol 𝑎 𝑧 𝑞 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{\left(a;q^{2}\right)_{n}% \left(b;q\right)_{n}}{\left(q^{2};q^{2}\right)_{n}\left(c;q\right)_{n}}z^{n}=% \frac{\left(b;q\right)_{\infty}\left(az;q^{2}\right)_{\infty}}{\left(c;q\right% )_{\infty}\left(z;q^{2}\right)_{\infty}}\sum_{n=0}^{\infty}\frac{\left(c/b;q% \right)_{2n}\left(z;q^{2}\right)_{n}b^{2n}}{\left(q;q\right)_{2n}\left(az;q^{2% }\right)_{n}}+\frac{\left(b;q\right)_{\infty}\left(azq;q^{2}\right)_{\infty}}{% \left(c;q\right)_{\infty}\left(zq;q^{2}\right)_{\infty}}\sum_{n=0}^{\infty}% \frac{\left(c/b;q\right)_{2n+1}\left(zq;q^{2}\right)_{n}b^{2n+1}}{\left(q;q% \right)_{2n+1}\left(azq;q^{2}\right)_{n}}.}}
    0 references
    DLMF id
    DLMF:17.9.E19
    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.m2aidec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1rdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1idec
    0 references
     
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