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Algorithmic Methods for Mixed Recurrence Equations, Zeros of Classical Orthogonal Polynomials and Classical Orthogonal Polynomial Solutions of Three-Term Recurrence Equations
Using an algorithmic approach, we derive classes of mixed recurrence equations satisfied by classical orthogonal polynomials. Starting from certain structure relations satisfied by classical orthogonal polynomials or their connection formulae, we show that our mixed recurrence equations are structurally valid. However, they couldn't be easily obtained with classical methods and for this reason, our algorithmic approach is important. The main algorithmic tool used here is an extended version of Zeilberger's ...