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

${\displaystyle p_{n}(t^{2})=(a+b)_{n}(a+c)_{n}(a+d)_{n}{}_{4}F_{3}\left({\begin{matrix}-n&a+b+c+d+n-1&a-t&a+t\\a+b&a+c&a+d\end{matrix}};1\right).}$

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 0579561
• Koornwinder, T.H. (2001) [1994], "Wilson polynomials", Encyclopedia of Mathematics, EMS Press