:03

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{h_n}{h_0 (\Jacobi{\alpha}{\beta}{n}@{1})^2}= \frac{n+\alpha+\beta+1}{2n+\alpha+\beta+1} \frac{\pochhammer{\beta+1}{n} n!}{\pochhammer{\alpha+1}{n} \pochhammer{\alpha+\beta+2}{n}} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{h_n}{h_0}= \frac{n+\alpha+\beta+1}{2n+\alpha+\beta+1} \frac{\pochhammer{\alpha+1}{n}\pochhammer{\beta+1}{n}}{\pochhammer{\alpha+\beta+2}{n} n!} h_0 = \frac{n+\alpha+\beta+1}{2n+\alpha+\beta+1} \frac{\pochhammer{\alpha+1}{n}\pochhammer{\beta+1}{n}}{\pochhammer{\alpha+\beta+2}{n} n!} h_0}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{h_n}{h_0} =\frac{2^{\alpha+\beta+1}\EulerGamma@{\alpha+1}\EulerGamma@{\beta+1}}{\EulerGamma@{\alpha+\beta+2}} =\frac{2^{\alpha+\beta+1}\EulerGamma@{\alpha+1}\EulerGamma@{-\alpha-\beta-1}}{\EulerGamma@{-\beta}}}}


Proof

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Symbols List

& : logical and
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
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 \Gamma}}  : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section of KLS.

URL links

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