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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11715 / rank
 
Normal rank
Property / Symbols used: Q11715 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11715 / qualifier
 
xml-id: C17.S1.XMD1.m1cdec

Revision as of 15:04, 2 January 2020

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DLMF:17.7.E23
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    Statements

    Defining formula
    ( 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}.}}
    0 references
    DLMF id
    DLMF:17.7.E23
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    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.m2addec
    0 references
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6atdec
    0 references
    Q11715
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1cdec
    0 references
     
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