Computer Algebra Algorithms for Orthogonal Polynomials and Special Functions

5-hour minicourse at the Euro
Summer School in Orthogonal Polynomials and Special Functions

Leuven, Belgium, August 12-17, 2002

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 binomial(n,k)*x^k/k!)
- the computation of generating 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 P(n,x)=sum(binomial(n,k)*binomial(-n-1,k)*((1-x)/2)^k,k=0..n)) (Zeilberger's algorithm)
- the computation of hypergeometric term representations of series (Zeilberger's and Petkovsek's algorithm)
- the verification of identities for (holonomic) special functions
- the detection of identities for orthogonal polynomials and special functions
- the identification of classical orthogonal polynomials, given by recurrence equations