Asymptotics for Sobolev orthogonal polynomials with coherent pairs: The Jacobi case, type 1

Author:
K. Pan

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2377-2388

MSC (1991):
Primary 42C05

MathSciNet review:
1443401

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Abstract: Define and as the th monic orthogonal polynomials with respect to and respectively. The pair is called a coherent pair if there exist non-zero constants such that

One can divide the coherent pairs into two cases: the Jacobi case and the Laguerre case. There are two types for each case: type 1 and 2. We investigate the asymptotic properties and zero distribution of orthogonal polynomials with respect to Sobolev inner product

for the coherent pair : the Jacobi case, type 1.

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Additional Information

**K. Pan**

Affiliation:
Department of Mathematics, Barry University, Miami Shores, Florida 33161

Email:
pan@euclid.barry.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04300-7

Received by editor(s):
July 24, 1996

Received by editor(s) in revised form:
January 22, 1997

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1998
American Mathematical Society