Formula:KLS:14.05:02

<< Formula:KLS:14.05:01

formula in Big q-Jacobi

Formula:KLS:14.05:03 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_{cq}^{aq}\frac{\qPochhammer{a^{-1}x,c^{-1}x}{q}{\infty}}{\qPochhammer{x,bc^{-1}x}{q}{\infty}} \bigqJacobi{m}@{x}{a}{b}{c}{q}\bigqJacobi{n}@{x}{a}{b}{c}{q}\,d_qx {}=aq(1-q)\frac{\qPochhammer{q,abq^2,a^{-1}c,ac^{-1}q}{q}{\infty}}{\qPochhammer{aq,bq,cq,abc^{-1}q}{q}{\infty}} {}\frac{(1-abq)}{(1-abq^{2n+1})} \frac{\qPochhammer{q,bq,abc^{-1}q}{q}{n}}{\qPochhammer{aq,abq,cq}{q}{n}}(-acq^2)^nq^{\binomial{n}{2}}\,\Kronecker{m}{n} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P_{n}}}  : big Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:01

formula in Big q-Jacobi

Formula:KLS:14.05:03 >>