A partial-sum deformation for a family of orthogonal polynomials

2024/08/30 by Erik Koelink, Koelink, Erik, Pablo Román +3 · 3 citations
Mathematics · #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2409.00261

Abstract

There are several questions one may ask about polynomials q_m(x)=q_m(x;t)=∑_n=0^mt^mp_n(x) attached to a family of orthogonal polynomials \p_n(x)\_n≥0. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of q_m(x;t) in the case of varying real parameter t.

Cited by

• Zeros of linear combinations of Laguerre polynomials
• Zeros of linear combinations of Hermite polynomials
• Zeros of linear combinations of orthogonal polynomials

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