Formula:KLS:14.10:72

<< Formula:KLS:14.10:71

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:73 >>

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

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle n=1,2,3,\ldots}}

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{cos}}}  : cosine function : http://dlmf.nist.gov/4.14#E2
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle T_{n}}}  : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8

Bibliography

Equation in Section 14.10 of KLS.

URL links

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<< Formula:KLS:14.10:71

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:73 >>