Formula:KLS:14.01:15
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicAskeyWilson{n}@@{x}{a}{b}{c}{d}{q}=\monicAskeyWilson{n+1}@@{x}{a}{b}{c}{d}{q}+\frac{1}{2}\left[a+a^{-1}-(A_n+C_n)\right]\monicAskeyWilson{n}@@{x}{a}{b}{c}{d}{q}+ \frac{1}{4}A_{n-1}C_n\monicAskeyWilson{n-1}@@{x}{a}{b}{c}{d}{q} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=\frac{a(1-q^n)(1-bcq^{n-1})(1-bdq^{n-1})(1-cdq^{n-1})}{(1-abcdq^{2n-2})(1-abcdq^{2n-1})}}}
&
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-abq^n)(1-acq^n)(1-adq^n)(1-abcdq^{n-1})}{a(1-abcdq^{2n-1})(1-abcdq^{2n})}}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-abq^n)(1-acq^n)(1-adq^n)(1-abcdq^{n-1})}{a(1-abcdq^{2n-1})(1-abcdq^{2n})}}}
Proof
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Symbols List
& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {\widehat p}_{n}}}
: monic Askey-Wilson polynomial : http://drmf.wmflabs.org/wiki/Definition:monicAskeyWilson
Bibliography
Equation in Section 14.1 of KLS.
URL links
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