Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis

2024/04/03 by C. Féliz-Sánchez, Carlos Féliz-Sánchez, H. Pijeira-Cabrera +3
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CA #math.CV #msc:30C15 #msc:33C45 #msc:42C05

paper · pdf · doi:10.3390/math12071082

published as Mathematics (2024), 12(7), 1082

openalex publication_date 2024/04/03 · openalex created_date 2024/04/04 · openalex updated_date 2026/07/23 · arxiv created 2026/07/28 · arxiv updated 2026/07/30

Abstract

Given a sequence of orthogonal polynomials Lnn=0∞, orthogonal with respect to a positive Borel ν measure supported on R+, let Qnn=0∞ be the the sequence of orthogonal polynomials with respect to the modified measure r(x)dν(x), where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula Qn(d)(z)Ln(d)(z)⇉n∏k=1N1ak+iz+akAk∏j=1N2z+bjbj+iBj, on compact subsets of C∖R+, where ak and bj are the zeros and poles of r, and the Ak, Bj are their respective multiplicities.

Citations

• Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product
• The Curious History of Faa di Bruno's Formula

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