# Definition:Racah

The LaTeX DLMF and DRMF macro \Racah represents the Racah polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\Racah{n} produces $\displaystyle {\displaystyle \Racah{n}}$
\Racah{n}@{x}{\alpha}{\beta}{\gamma}{\delta} produces $\displaystyle {\displaystyle \Racah{n}@{x}{\alpha}{\beta}{\gamma}{\delta}}$

These are defined by $\displaystyle {\displaystyle \Racah{n}@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} {}:=\HyperpFq{4}{3}@@{-n,n+\alpha+\beta+1,-x,x+\gamma+\delta+1}{\alpha+1,\beta+\delta+1,\gamma+1}{1}, }$

where $\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1), }$ and $\displaystyle \alpha+1=-N$ or $\displaystyle \beta+\delta+1=-N$ or $\displaystyle \gamma+1=-N$ with $\displaystyle N$ a nonnegative integer.

## Symbols List

$\displaystyle {\displaystyle R_{n}}$  : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4
$\displaystyle {\displaystyle {{}_{p}F_{q}}}$  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1