DLMF:17.7.E23 (Q5419): Difference between revisions

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Property / Symbols used: Q10768 / rank
 
Normal rank
Property / Symbols used: Q10768 / qualifier
 
Defining formula:

δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

\Kroneckerdelta{\NVar{j}}{\NVar{k}}
Property / Symbols used: Q10768 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r4.m5adec

Revision as of 15:04, 2 January 2020

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DLMF:17.7.E23
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    Statements

    ( 1 - a q ) ( 1 - b q ) k = 0 n ( a p k , b p - k ; q ) n - 1 ( 1 - ( a p 2 k / b ) ) ( p ; p ) n ( p ; p ) n - k ( a p k / b ; q ) n + 1 ( - 1 ) k p ( k 2 ) = δ n , 0 . 1 𝑎 𝑞 1 𝑏 𝑞 superscript subscript 𝑘 0 𝑛 q-multiple-Pochhammer 𝑎 superscript 𝑝 𝑘 𝑏 superscript 𝑝 𝑘 𝑞 𝑛 1 1 𝑎 superscript 𝑝 2 𝑘 𝑏 q-Pochhammer-symbol 𝑝 𝑝 𝑛 q-Pochhammer-symbol 𝑝 𝑝 𝑛 𝑘 q-Pochhammer-symbol 𝑎 superscript 𝑝 𝑘 𝑏 𝑞 𝑛 1 superscript 1 𝑘 superscript 𝑝 binomial 𝑘 2 Kronecker 𝑛 0 {\displaystyle{\displaystyle\left(1-\frac{a}{q}\right)\left(1-\frac{b}{q}% \right)\sum_{k=0}^{n}\frac{\left(ap^{k},bp^{-k};q\right)_{n-1}(1-(ap^{2k}/b))}% {\left(p;p\right)_{n}\left(p;p\right)_{n-k}\left(ap^{k}/b;q\right)_{n+1}}(-1)^% {k}p^{\genfrac{(}{)}{0.0pt}{}{k}{2}}=\delta_{n,0}.}}
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    DLMF:17.7.E23
    0 references
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    introduction.Sx4.p1.t1.r4.m5adec
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