Formula:KLS:09.02:13: Difference between revisions
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Latest revision as of 08:34, 22 December 2019
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}=\monicRacah{n+1}@@{x}{\alpha}{\beta}{\gamma}{\delta}-(A_n+C_n)\monicRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}+A_{n-1}C_n\monicRacah{n-1}@@{x}{\alpha}{\beta}{\gamma}{\delta} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=\frac{n(n+\alpha+\beta-\gamma)(n+\alpha-\delta)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)} =\left\{\begin{array}{ll} \displaystyle\frac{n(n+\beta)(n+\beta-\gamma-N-1)(n-\delta-N-1)}{(2n+\beta-N-1)(2n+\beta-N)} &<br /> \quad\textrm{if}\quad\alpha+1=-N\\[5mm] \displaystyle\frac{n(n+\alpha+\beta+N+1)(n+\alpha+\beta-\gamma)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)} &<br /> \quad\textrm{if}\quad\beta+\delta+1=-N\\[5mm] \displaystyle\frac{n(n+\alpha+\beta+N+1)(n+\alpha-\delta)(n+\beta)}{(2n+\alpha+\beta)(2n+\alpha+\beta+1)} &<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 A_n=\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\beta+\delta+1)(n+\gamma+1)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} =\left\{\begin{array}{ll} \displaystyle\frac{(n+\beta-N)(n+\beta+\delta+1)(n+\gamma+1)(n-N)}{(2n+\beta-N)(2n+\beta-N+1)} &<br /> \quad\textrm{if}\quad\alpha+1=-N\\[5mm] \displaystyle\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\gamma+1)(n-N)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} &<br /> \quad\textrm{if}\quad\beta+\delta+1=-N\\[5mm] \displaystyle\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\beta+\delta+1)(n-N)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} &<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 A_n=\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\beta+\delta+1)(n+\gamma+1)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} =\left\{\begin{array}{ll} \displaystyle\frac{(n+\beta-N)(n+\beta+\delta+1)(n+\gamma+1)(n-N)}{(2n+\beta-N)(2n+\beta-N+1)} &<br /> \quad\textrm{if}\quad\alpha+1=-N\\[5mm] \displaystyle\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\gamma+1)(n-N)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} &<br /> \quad\textrm{if}\quad\beta+\delta+1=-N\\[5mm] \displaystyle\frac{(n+\alpha+1)(n+\alpha+\beta+1)(n+\beta+\delta+1)(n-N)}{(2n+\alpha+\beta+1)(2n+\alpha+\beta+2)} &<br /> \quad\textrm{if}\quad\gamma+1=-N \end{array}\right.}} }
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 {\widehat R}_{n}}}
: monic Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicRacah
Bibliography
Equation in Section 9.2 of KLS.
URL links
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