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Wilson polynomials

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In mathematics, Wilson polynomials are a family of orthogonal polynomials introduced by {{harvs|txt|authorlink=James A. Wilson|first=James A. |last=Wilson|year=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

References

  • {{Citation | last1=Wilson | first1=James A. | title=Some hypergeometric orthogonal polynomials | doi=10.1137/0511064 |mr=579561 | year=1980 | journal=SIAM Journal on Mathematical Analysis | issn=0036-1410 | volume=11 | issue=4 | pages=690–701}}
  • {{eom|id=Wilson_polynomials|title=Wilson polynomials|first=T.H. |last=Koornwinder}}

Category:Hypergeometric functions

Category:Orthogonal polynomials

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