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

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dc.contributor.authorCarlos FΓ©liz SΓ‘nchez
dc.date.accessioned2025-09-04T20:49:25Z
dc.date.available2025-09-04T20:49:25Z
dc.date.issued2024-04-03
dc.descriptionPublicado por la revista: "Mathematics. 2024, 12, 1082. "
dc.description.abstractGiven a sequence of orthogonal polynomials {𝐿𝑛}βˆžπ‘›=0, orthogonal with respect to a positive Borel 𝜈 measure supported on ℝ+, let {𝑄𝑛}βˆžπ‘›=0 be the the sequence of orthogonal polynomials with respect to the modified measure π‘Ÿ(π‘₯)π‘‘πœˆ(π‘₯), where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula 𝑄(𝑑)𝑛(𝑧)𝐿(𝑑)𝑛(𝑧)β‡‰π‘›βˆπ‘1π‘˜=1(π‘Žπ‘˜βˆš+π‘–π‘§βˆš+π‘Žπ‘˜βˆš)π΄π‘˜βˆπ‘2𝑗=1(π‘§βˆš+π‘π‘—βˆšπ‘π‘—βˆš+𝑖)𝐡𝑗, on compact subsets of β„‚βˆ–β„+, where π‘Žπ‘˜ and 𝑏𝑗 are the zeros and poles of r, and the π΄π‘˜, 𝐡𝑗 are their respective multiplicities.
dc.identifier.citationSΓ‘nchez, C. F. (2024). Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis. βˆ‘Mathematics, 12, 1082.
dc.identifier.urihttps://repositoriovip.uasd.edu.do/handle/123456789/1045
dc.language.isoen
dc.relation.ispartofseries2024; 25
dc.titleAsymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
dc.typeArticle
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