Formula:KLS:14.02:23

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{\nabla\left[{\tilde w}(x;\alpha,\beta,\gamma,\delta|q)\qRacah{n}@{\mu(x)}{\alpha}{\beta}{\gamma}{\delta}{q}\right]}{\nabla\mu(x)} {}=\frac{1}{(1-q)(1-\gamma\delta)}{\tilde w}(x;\alpha q^{-1},\beta q^{-1},\gamma q^{-1},\delta|q) {} \qRacah{n+1}@{\mu(x)}{\alpha q^{-1}}{\beta q^{-1}}{\gamma q^{-1}}{\delta}{q} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =\lambda(x)=q^{-x}+cq^{x-N} =q^{-x}+q^{x+\gamma+\delta+1} =2a\cos@@{\theta}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1)}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x):=q^{-x}+\gamma\delta q^{x+1}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =\lambda(x)=q^{-x}+cq^{x-N} =q^{-x}+q^{x+\gamma+\delta+1} =2a\cos@@{\theta}}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1)}}


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 R_{n}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Racah polynomial : http://dlmf.nist.gov/18.28#E19
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{cos}}}  : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 14.2 of KLS.

URL links

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