In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients.
The Racah polynomials were first defined by and are given by
Orthogonality
when , where is the Racah polynomial,
is the Kronecker delta function and the weight functions are
and
is the Pochhammer symbol.
Rodrigues-type formula
where is the backward difference operator,
Generating functions There are three generating functions for when or
when or
when or
Connection formula for Wilson polynomials When
where are Wilson polynomials.
q-analog introduced the q-Racah polynomials defined in terms of basic hypergeometric functions by
They are sometimes given with changes of variables as
References