Formula:KLS:14.05:78

<< Formula:KLS:14.05:77

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:79 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qHyperrphis{2}{1}@@{qx^{-1},0}{q}{q}{xt}\,\qHyperrphis{1}{1}@@{c^{-1}x}{q}{q}{cqt} =\sum_{n=0}^{\infty}\frac{\qPochhammer{cq}{q}{n}}{\qPochhammer{q,q}{q}{n}}\bigqLegendre{n}@{x}{c}{q}t^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 {{}_{r}\phi_{s}}}}  : basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
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}}}  : big Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLegendre

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:77

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:79 >>