Formula:KLS:09.08:21

<< Formula:KLS:09.08:20

formula in Jacobi: Special cases

Formula:KLS:09.08:24 >>

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

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{\cpi^\frac12 \EulerGamma@{\lambda+\frac12}}{\EulerGamma@{\lambda+1}} \frac{h_n}{h_0 (\Ultra{\lambda}{n}@{1})^2} = \frac\lambda{\lambda+n} \frac{n!}{\pochhammer{2\lambda}{n}}}}

Proof

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Symbols List

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 \pi}}  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C^{\mu}_{n}}}  : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:20

formula in Jacobi: Special cases

Formula:KLS:09.08:24 >>