Formula:KLS:14.08:34

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qinvAlSalamChihara{n}@{\frac12(aq^{-x}+a^{-1}q^x)}{a}{b }{q^{-1}} =(-ab^{-1})^x q^{-\frac12 x(x+1)} \frac{\qPochhammer{qba^{-1}}{q}{x}}{\qPochhammer{a^{-1}b^{-1}}{q}{x}} \qHyperrphis{2}{1}@@{q^{-x},a^{-2}q^x}{qba^{-1}}{q}{q^{n+1}} }}

Proof

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Symbols List

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}} -inverse Al-Salam-Chihara polynomial : http://dlmf.nist.gov/23.1
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 {{}_{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

Bibliography

Equation in Section 14.8 of KLS.

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