Continuous dual Hahn polynomials

Template:Short description 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

Continuous Dual Hahn polynomials

$S_n(x^2;a,b,c)={}_3{F}_2(-n,a+ix,a-ix;a+b,a+c;1).$

Continuous Dual Hahn Polynomials, complex3d plot

Template:Harvs give a detailed list of their properties.

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

Relation to other polynomials

• Wilson polynomials are a generalization of continuous dual Hahn polynomials

References

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