Formula:KLS:14.02:12
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicqRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}=\monicqRacah{n+1}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}+\left[1+\gamma\delta q-(A_n+C_n)\right]\monicqRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}+A_{n-1}C_n\monicqRacah{n-1}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=\frac{q(1-q^n)(1-\beta q^n)(\gamma-\alpha\beta q^n)(\delta-\alpha q^n)} {(1-\alpha\beta q^{2n})(1-\alpha\beta q^{2n+1})}}}
&
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-\alpha q^{n+1})(1-\alpha\beta q^{n+1})(1-\beta\delta q^{n+1})(1-\gamma q^{n+1})} {(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-\alpha q^{n+1})(1-\alpha\beta q^{n+1})(1-\beta\delta q^{n+1})(1-\gamma q^{n+1})} {(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}}
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 R}_{n}}}
: monic Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqRacah
Bibliography
Equation in Section 14.2 of KLS.
URL links
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