Formula:KLS:09.08:04
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\Jacobi{\alpha}{\beta}{n}@{x}=\frac{2(n+1)(n+\alpha+\beta+1)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)}\Jacobi{\alpha}{\beta}{n+1}@{x} {}+\frac{\beta^2-\alpha^2}{(2n+\alpha+\beta)(2n+\alpha+\beta+2)}\Jacobi{\alpha}{\beta}{n}@{x} {}+\frac{2(n+\alpha)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)}\Jacobi{\alpha}{\beta}{n-1}@{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 P^{(\alpha,\beta)}_{n}}}
: Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
Bibliography
Equation in Section 9.8 of KLS.
URL links
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