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

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Property / 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<a<q^{-1},b<q^{-1}
Property / 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}}} / rank
 
Normal rank

Revision as of 17:03, 30 December 2019

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DLMF:18.27.E14
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    Statements

    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 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},}}
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    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