Formula:KLS:09.02:07

<< Formula:KLS:09.02:05

formula in Racah

Formula:KLS:09.02:08 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)\Racah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} =A_n\Racah{n+1}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}-\left(A_n+C_n\right)\Racah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}+C_n\Racah{n-1}@@{\lambda(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 \lambda(x)=x(x+\gamma+\delta+1)}}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

& : logical and
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

Bibliography

Equation in Section 9.2 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.02:05

formula in Racah

Formula:KLS:09.02:08 >>