Zeros of linear combinations of Laguerre polynomials from different sequences

Authors:
Kathy Driver;Kerstin Jordaan
Affiliations:
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch 7701, Cape Town, South Africa;Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
Cited 2

Quasi-orthogonality with applications to some families of classical orthogonal polynomials

Applied Numerical Mathematics
Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

Numerische Mathematik

Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

Applied Numerical Mathematics
Full length article: Interlacing of zeros of orthogonal polynomials under modification of the measure

Journal of Approximation Theory

Quantified Score

Hi-index	7.29

Visualization

Abstract

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely R"n=L"n^@a+aL"n^@a^^^' and S"n=L"n^@a+bL"n"-"1^@a^^^'. Proofs and numerical counterexamples are given in situations where the zeros of R"n, and S"n, respectively, interlace (or do not in general) with the zeros of L"k^@a, L"k^@a^^^', k=n or n-1. The results we prove hold for continuous, as well as integral, shifts of the parameter @a.