Matrix Pearson equations satisfied by Koornwinder weights in two variables Articles uri icon

publication date

  • February 2018

start page

  • 81

end page

  • 100

issue

  • 1

volume

  • 153

international standard serial number (ISSN)

  • 0167-8019

electronic international standard serial number (EISSN)

  • 1572-9036

abstract

  • We consider Koornwinder's method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder's construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials.

keywords

  • orthogonal polynomials in two variables; koornwinder weights; partial differential equations; matrix pearson equations