Article · Wikipedia archive · Last revised Jun 4, 2026

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.

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In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by James Wilson1 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 ( − n a + b + c + d + n − 1 a − t a + t a + b a + c a + d ; 1 ) . {\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

See also

References

References

  1. Wilson, James A. (July 1980). "Some Hypergeometric Orthogonal Polynomials". SIAM Journal on Mathematical Analysis. 11 (4): 690–701. doi:10.1137/0511064. ISSN 0036-1410.
Further reading

Further reading