Harman Patil (Editor)

Continuous Hahn polynomials

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In mathematics, the continuous 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

p n ( x ; a , b , c , d ) = i n ( a + c ) n ( a + d ) n n ! 3 F 2 ( − n , n + a + b + c + d − 1 , a + i x ; a + c , a + d ; 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 Hahn polynomials, and the continuous dual Hahn polynomials Sn(x;a,b,c). 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, a generalization of continuous Hahn polynomials

    • References

    Continuous Hahn polynomials Wikipedia
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