Wilson polynomials

In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by James Wilson 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

Further reading

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

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