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Continuous dual Hahn polynomials

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Continuous dual Hahn polynomials

In mathematics, the continuous dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by

S n ( x 2 ; a , b , c ) = 3 F 2 ( − n , a + i x , a − i x ; a + b , a + c ; 1 ) .  

Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Closely related polynomials include the dual Hahn polynomials Rn(x;γ,δ,N), the continuous Hahn polynomials pn(x,a,b, a, b), and the Hahn polynomials. These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Qn(x;α,β, N;q), and so on.

Relation to other polynomials

  • Wilson polynomials are a generalization of continuous dual Hahn polynomials

    • References

    Continuous dual Hahn polynomials Wikipedia
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