Formula:KLS:14.10:51

<< Formula:KLS:14.10:47

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:52 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_q\ctsqUltra{n}@{x}{\beta}{q}=-q^{-\frac{1}{2}n}(1-\beta)(\expe^{\iunit\theta}-\expe^{-\iunit\theta}) \ctsqUltra{n-1}@{x}{\beta q}{q} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x=\cos@@{\theta}}}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_{n}}}  : continuous Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{i}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i
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 14.10 of KLS.

URL links

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<< Formula:KLS:14.10:47

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:52 >>