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Orthogonal polynomials and recurrence equations, operator equations and factorization

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

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Citation
In: Mathematische Schriften Kassel 05, 14 / (2005) , S. ;
@article{urn:nbn:de:hebis:34-200604069128,
  author    ={Koepf, Wolfram},
  title    ={Orthogonal polynomials and recurrence equations, operator equations and factorization},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2005}
}