Representations of orthogonal polynomials (Q1392783)

The paper gives extensions of earlier results of the authors by presenting a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation of a given orthogonal polynomial is possible. An algorithm for computing recurrence relations for connection coefficients is given. Zeilberger's algorithm and further versions of this algorithm are important tools in this work.