Zeros of linear combinations of Laguerre polynomials from different sequences

[摘要] We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely R(n) = L(n)(alpha) + aL(n)(alpha') and S(n) = L(n)(alpha) + bL(n-1)(alpha'). Proofs and numerical counter examples 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)(alpha), L(k)(alpha'), k = n or n - 1. The results we prove hold for continuous, as well as integral, shifts of the parameter alpha. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2009-12-01

[效力级别]  Proceedings Paper

[关键词] Laguerre polynomials;Zeros;Interlacing properties;Linear combinations