Formula:KLS:14.06:02

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{x=0}^N\frac{\qPochhammer{\alpha q,q^{-N}}{q}{x}}{\qPochhammer{q,\beta^{-1}q^{-N}}{q}{x}}(\alpha\beta q)^{-x} \qHahn{m}@{q^{-x}}{\alpha}{\beta}{N}{q}\qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}{q} {}=\frac{\qPochhammer{\alpha\beta q^2}{q}{N}}{\qPochhammer{\beta q}{q}{N}(\alpha q)^N} \frac{\qPochhammer{q,\alpha\beta q^{N+2},\beta q}{q}{n}}{\qPochhammer{\alpha q,\alpha\beta q,q^{-N}}{q}{n}}\ \frac{(1-\alpha\beta q)(-\alpha q)^n}{(1-\alpha\beta q^{2n+1})} q^{\binomial{n}{2}-Nn}\,\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 Q_{n}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
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 14.6 of KLS.

URL links

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