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Duplication coefficients via generating functions

Chaggara, Hamza
Koepf, Wolfram

In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.

Citation
In: Mathematische Schriften Kassel 06, 05 / (2006) , S. ; 
@article{urn:nbn:de:hebis:34-2006110915657,
  author    ={Chaggara, Hamza and Koepf, Wolfram},
  title    ={Duplication coefficients via generating functions},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2006}
}