Wilson polynomials

In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by James A. Wilson (1980) that generalize Jacobi polynomials, Hahn polynomials, and Charlier polynomials.

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

p_n(t^2)=(a+b)_n(a+c)_n(a+d)_n {}_4F_3\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

Askey-Wilson polynomials are a q-analogue of Wilson polynomials.

References

Wilson, James A. (1980), "Some hypergeometric orthogonal polynomials", SIAM Journal on Mathematical Analysis 11 (4): 690–701, doi:10.1137/0511064, ISSN 0036-1410, MR 579561
Koornwinder, T.H. (2001), "Wilson polynomials", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4