Formula:KLS:14.10:85

<< Formula:KLS:14.10:84

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:86 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lim_{q\uparrow1} \ctsqUltra{2m}@{x}{-q^\lambda }{ -q}= \frac{\pochhammer{\lambda}{m}}{\pochhammer{\frac12\lambda}{m}} \Jacobi{\frac12\lambda}{\frac12\lambda-1}{m}@{2x^2-1} }}

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 (a)_n}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P^{(\alpha,\beta)}_{n}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 14.10 of KLS.

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<< Formula:KLS:14.10:84

formula in Continuous q-Jacobi: Special cases

Formula:KLS:14.10:86 >>