Formula:KLS:09.02:04: Difference between revisions

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Latest revision as of 07:34, 22 December 2019


Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{x=0}^N\frac{\pochhammer{\alpha+1}{x}\pochhammer{\beta+\delta+1}{x}\pochhammer{\gamma+1}{x}\pochhammer{\gamma+\delta+1}{x}\pochhammer{(\gamma+\delta+3)/2}{x}} {\pochhammer{-\alpha+\gamma+\delta+1}{x}\pochhammer{-\beta+\gamma+1}{x}\pochhammer{(\gamma+\delta+1)/2}{x}\pochhammer{\delta+1}{x}x!} {} \Racah{m}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}\Racah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} {}=M\frac{\pochhammer{n+\alpha+\beta+1}{n}\pochhammer{\alpha+\beta-\gamma+1}{n}\pochhammer{\alpha-\delta+1}{n}\pochhammer{\beta+1}{n}n!} {\pochhammer{\alpha+\beta+2}{2n}\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{\gamma+1}{n}}\,\Kronecker{m}{n} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle M=\left\{\begin{array}{ll} \displaystyle\frac{\pochhammer{-\beta}{N}\pochhammer{\gamma+\delta+2}{N}}{\pochhammer{-\beta+\gamma+1}{N}\pochhammer{\delta+1}{N}} &<br /> \quad\textrm{if}\quad\alpha+1=-N\\[5mm] \displaystyle\frac{\pochhammer{-\alpha+\delta}{N}\pochhammer{\gamma+\delta+2}{N}}{\pochhammer{-\alpha+\gamma+\delta+1}{N}\pochhammer{\delta+1}{N}} &<br /> \quad\textrm{if}\quad\beta+\delta+1=-N\\[5mm] \displaystyle\frac{\pochhammer{\alpha+\beta+2}{N}\pochhammer{-\delta}{N}}{\pochhammer{\alpha-\delta+1}{N}\pochhammer{\beta+1}{N}} &<br /> \quad\textrm{if}\quad\gamma+1=-N \end{array}\right.}} } &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1)}}


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 \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
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 R_{n}}}  : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 9.2 of KLS.

URL links

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