Definition:monicRacah

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

This macro is in the category of polynomials.

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

\monicRacah{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}}}}$

\monicRacah{n}@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}\!\left(\lambda(x);\alpha,\beta,\gamma,\delta\right)}}}$

\monicRacah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}\!\left(\lambda(x)\right)}}}$

These are defined by

${\displaystyle{\displaystyle R_{n}\!\left(\lambda(x);\alpha,\beta,\gamma,\delta\right)=:\frac{{\left(n+\alpha+\beta+1\right)_{n}}}{{\left(\alpha+1\right)_{n}}{\left(\beta+\delta+1\right)_{n}}{\left(\gamma+1\right)_{n}}}{\widehat{R}}_{n}\!\left(\lambda(x)\right).}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}}}}$ : monic Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicRacah
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

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