Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
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Date
2024-04-03
Authors
Carlos FΓ©liz SΓ‘nchez
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Abstract
Given a sequence of orthogonal polynomials {πΏπ}βπ=0, orthogonal with respect to a positive Borel π measure supported on β+, let {ππ}βπ=0 be the the sequence of orthogonal polynomials with respect to the modified measure π(π₯)ππ(π₯), where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula π(π)π(π§)πΏ(π)π(π§)βπβπ1π=1(ππβ+ππ§β+ππβ)π΄πβπ2π=1(π§β+ππβππβ+π)π΅π, on compact subsets of βββ+, where ππ and ππ are the zeros and poles of r, and the π΄π, π΅π are their respective multiplicities.
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Publicado por la revista: "Mathematics. 2024, 12, 1082. "
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SΓ‘nchez, C. F. (2024). Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis. βMathematics, 12, 1082.