Quintero Roba, Javier AlejandroPijeira Cabrera, Héctor EstebanFéliz Sánchez, Carlos2024-10-162024-10-162024-04-03Féliz-Sánchez, C.; Pijeira-Cabrera, H.; Quintero-Roba, J. Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis. Mathematics 2024, 12, 1082. https://doi.org/10.3390/math120710822227-7390 (online)https://hdl.handle.net/10115/40260Given a sequence of orthogonal polynomials { L n } n = 0 ∞ , orthogonal with respect to a positive Borel ν measure supported on R + , let { Q n } n = 0 ∞ be the the sequence of orthogonal polynomials with respect to the modified measure r ( x ) d ν ( x ) , where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula Q n ( d ) ( z ) L n ( d ) ( z ) ⇉ n ∏ k = 1 N 1 a k + i z + a k A k ∏ j = 1 N 2 z + b j b j + i B j , on compact subsets of C ∖ R + , where a k and b j are the zeros and poles of r, and the A k , B j are their respective multiplicitiesengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/orthogonal polynomialsasymptotic behaviorrational modificationsinfo:eu-repo/semantics/article10.3390/math12071082info:eu-repo/semantics/openAccess