Computer Algebra Algorithms for Orthogonal Polynomials and Special Functions

In this minicourse I would like to present computer algebra algorithms for the work with orthogonal polynomials and special functions. This includes • the computation of power series representations of hypergeometric type functions, given by “expressions”, like arcsin(x)/x , • the computation of holonomic differential equations for functions, given by expressions, • the computation of holonomic recurrence equations for sequences, given by expressions, like ( n k ) x k! , • the identification of hypergeometric functions, • the computation of antidifferences of hypergeometric terms (Gosper’s algorithm), • the computation of holonomic differential and recurrence equations for hypergeometric series, given the series summand, like