11/10/2018, Room 27, 14:30 hs FAMAF
Burchnall type identities for orthogonal polynomials
Speaker: Erik Koelink
Abstract:
L.J. Burchnall (1892-1975) proved a converse to the linearization formula for Hermite polynomials in 1941. In doing so, he calculated powers of a differential operator in terms of Hermite polynomials and (standard) derivatives. We show that this approach generalizes to all families of orthogonal polynomials in the Askey-scheme and its $q$- analog. We discuss several applications of this approach. One application lies in expansion formulas, and a related application is related to the Lax pair formalism for the Toda lattice.
It is possible to extend this approach to some families of matrix-valued orthogonal polynomials and
a corresponding non-abelian Toda lattice. The lecture reports on joint work with Mourad Ismail (University of Central Florida, USA) and Pablo Román (UNC).
It is possible to extend this approach to some families of matrix-valued orthogonal polynomials and
a corresponding non-abelian Toda lattice. The lecture reports on joint work with Mourad Ismail (University of Central Florida, USA) and Pablo Román (UNC).