Higher Order Coherent Pairs Articles uri icon

publication date

  • October 2012

start page

  • 105

end page

  • 135

issue

  • 1

volume

  • 121

International Standard Serial Number (ISSN)

  • 0167-8019

Electronic International Standard Serial Number (EISSN)

  • 1572-9036

abstract

  • In this paper, we study necessary and sufficient conditions for the relation , where {P (n) (x)} (na parts per thousand yen0) and {R (n) (x)} (na parts per thousand yen0) are two sequences of monic orthogonal polynomials with respect to the quasi-definite linear functionals , respectively, or associated with two positive Borel measures mu (0),mu (1) supported on the real line. We deduce the connection with Sobolev orthogonal polynomials, the relations between these functionals as well as their corresponding formal Stieltjes series. As sake of example, we find the coherent pairs when one of the linear functionals is classical.