Formula:KLS:14.12:02

<< Formula:KLS:14.12:01

formula in Little q-Jacobi

Formula:KLS:14.12:03 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{k=0}^{\infty}\frac{\qPochhammer{bq}{q}{k}}{\qPochhammer{q}{q}{k}}(aq)^k\littleqJacobi{m}@{q^k}{a}{b}{q}\littleqJacobi{n}@{q^k}{a}{b}{q} {}=\frac{\qPochhammer{abq^2}{q}{\infty}}{\qPochhammer{aq}{q}{\infty}}\frac{(1-abq)(aq)^n}{(1-abq^{2n+1})} \frac{\qPochhammer{q,bq}{q}{n}}{\qPochhammer{aq,abq}{q}{n}}\,\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 \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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}}}  : little 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:littleqJacobi
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 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:01

formula in Little q-Jacobi

Formula:KLS:14.12:03 >>