Wilson polynomials explained

In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by that generalize Jacobi polynomials, Hahn polynomials, and Charlier polynomials.

They are defined in terms of the generalized hypergeometric function and the Pochhammer symbols by

2)=(a+b)
p
n(a+c)

n(a+d)n{}4F3\left(\begin{matrix}-n&a+b+c+d+n-1&a-t&a+t\a+b&a+c&a+d\end{matrix};1\right).

See also