Formula:KLS:14.05:42

<< Formula:KLS:14.05:41

formula in Big q-Jacobi

Formula:KLS:14.05:43 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \bigqJacobiIVparam{n}@{x}{a}{b}{c}{d}{q} =(qac^{-1}x)^n \frac{\qPochhammer{qb,q}{q}{n}}{\qPochhammer{-qac^{-1}d}{q}{n}} \sum_{k=0}^n\frac{\qPochhammer{cx^{-1}}{q}{n-k}}{\qPochhammer{q,qa}{q}{n-k}} \frac{\qPochhammer{-qbd^{-1}x}{q}{k}}{\qPochhammer{qb,q}{q}{k}} (-1)^k q^{\frac12 k(k-1)}(-dx^{-1})^k }}

Proof

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Symbols List

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 with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam
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 \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:41

formula in Big q-Jacobi

Formula:KLS:14.05:43 >>