Wilson polynomials

Template:Format footnotes In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by Template:Harvs that generalize Jacobi polynomials, Hahn polynomials, and Charlier polynomials.

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

$p_n(t^2)=(a+b{)}_n(a+c{)}_n(a+d{)}_n{}_4{F}_3(\begin{array}{cccc}-n& a+b+c+d+n-1& a-t& a+t\\ a+b& a+c& a+d\end{array};1).$

See also

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

References

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• Template:Eom

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