DLMF:18.27.E14 (Q5965): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
test:

( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2adec

Revision as of 00:49, 2 January 2020

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DLMF:18.27.E14
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    Statements

    test
    ∑ y = 0 ∞ p n ⁢ ( q y ) ⁢ p m ⁢ ( q y ) ⁢ ( b ⁢ q ; q ) y ⁢ ( a ⁢ q ) y ( q ; q ) y = h n ⁢ δ n , m , superscript subscript 𝑦 0 subscript 𝑝 𝑛 superscript 𝑞 𝑦 subscript 𝑝 𝑚 superscript 𝑞 𝑦 q-Pochhammer-symbol 𝑏 𝑞 𝑞 𝑦 superscript 𝑎 𝑞 𝑦 q-Pochhammer-symbol 𝑞 𝑞 𝑦 subscript ℎ 𝑛 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\sum_{y=0}^{\infty}p_{n}(q^{y})p_{m}(q^{y})\frac{% \left(bq;q\right)_{y}(aq)^{y}}{\left(q;q\right)_{y}}=h_{n}\delta_{n,m},}}
    0 references
    DLMF id
    DLMF:18.27.E14
    0 references
    constraint
    0 < a < q - 1 , b < q - 1 formulae-sequence 0 𝑎 superscript 𝑞 1 𝑏 superscript 𝑞 1 {\displaystyle{\displaystyle 0<a<q^{-1},b<q^{-1}}}
    0 references
    Symbols used
    Q10768
    test
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5abdec
    0 references
    Q11298
    test
    ( 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
     
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