Polynomial solutions of differential-difference equations or Much Ado About Nothing (Dr. Diego Dominici)
Sprache des Titels:
Abstract: We present some results about certain families of polynomials
arising as solutions of equations with mixed differential and difference
operators. Some of these polynomials are related to combinatorial
sequences and others appear in problems from the theory of Special
Functions. In many cases, the complexity of the problem can only be
attacked using symbolic computation.
We will show techniques for analyzing their asymptotic behavior and the
location and interlacing of their zeros. But more importantly, we will
show that much remains to be done and will offer a rich (we hope)
selection of open problems.
Parts of this work were conducted in collaboration with K. Driver
(University of Cape Town), K. Jordaan (University of Pretoria), C.
Knessl (University of Illinois at Chicago) and W. Van Assche (Katholieke