Orthogonal polynomials, special functions, and applications

S29. Special functions, orthogonal polynomials and applications

Algorithmic Work with Orthogonal Polynomials and Special Functions

In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can ...

FOCM 2014 - Workshop C5 Special Functions and Orthogonal Polynomials

Krall and exceptional polynomials are two of the more important extensions of the classical families of Hermite, Laguerre and Jacobi. On the one hand, Krall or bispectral polynomials are orthogonal polynomials which are also eigenfunctions of a differential operator of order bigger than two (and polynomial coefficients). The first examples were introduced by H. Krall in 1940, and since the eigh...

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...

Identities for Families of Orthogonal Polynomials and Special Functions

In this article we present new results for families of orthogonal polynomials and special functions, that are determined by algorithmical approaches. In the first section, we present new results, especially for discrete families of orthogonal polynomials, obtained by an application of the celebrated Zeilberger algorithm. Next, we present algorithms for holonomic families f(n, x) of special func...