Formula:KLS:09.01:27

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formula in Wilson

Formula:KLS:09.01:28 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lim_{t\rightarrow\infty}\frac{\Wilson{n}@{\frac{1}{2}(1-x)t^2}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\beta+1)+\iunit t}{\frac{1}{2}(\beta+1}-\iunit t)}{t^{2n}n!} {}=\Jacobi{\alpha}{\beta}{n}@{x} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle W_{n}}}  : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2
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 P^{(\alpha,\beta)}_{n}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.1 of KLS.

URL links

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formula in Wilson

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