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dc.contributor.authorBagdasaryan, Armen G.
dc.contributor.authorBagdasar, Ovidiu
dc.date.accessioned2018-12-17T14:29:53Z
dc.date.available2018-12-17T14:29:53Z
dc.date.issued2018-12-06
dc.identifier.citationBagdasaryan, A.G., and Bagdasar, O. (2018) ‘On an arithmetic triangle of numbers arising from inverses of analytic functions’, Electronic Notes in Discrete Mathematics, 70, pp. 17-24. doi: 10.1016/j.endm.2018.11.003en
dc.identifier.issn1571-0653
dc.identifier.doi10.1016/j.endm.2018.11.003
dc.identifier.urihttp://hdl.handle.net/10545/623233
dc.description.abstractThe Lagrange inversion formula is a fundamental tool in combinatorics. In this work, we investigate an inversion formula for analytic functions, which does not require taking limits. By applying this formula to certain functions we have found an interesting arithmetic triangle for which we give a recurrence formula. We then explore the links between these numbers, Pascal’s triangle, and Bernoulli’s numbers, for which we obtain a new explicit formula. Furthermore, we present power series and asymptotic expansions of some elementary and special functions, and some links to the Online Encyclopedia of Integer Sequences (OEIS).
dc.description.sponsorshipO. Bagdasar’s research was supported by a grant of the Romanian National Authority for Research and Innovation, CNCS/CCCDI UEFISCDI, project number PN-III-P2-2.1-PED-2016-1835, within PNCDI III.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofseriesProceedings of TCDM'18en
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S1571065318301987en
dc.rightsArchived with thanks to Electronic Notes in Discrete Mathematicsen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectInversion formulaen
dc.subjectAnalytic functionsen
dc.subjectArithmetic triangleen
dc.subjectRecurrent sequencesen
dc.subjectBernoulli numbersen
dc.subjectInteger sequencesen
dc.titleOn an arithmetic triangle of numbers arising from inverses of analytic functions.en
dc.typeArticleen
dc.contributor.departmentAmerican University of the Middle Easten
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalElectronic Notes in Discrete Mathematicsen
html.description.abstractThe Lagrange inversion formula is a fundamental tool in combinatorics. In this work, we investigate an inversion formula for analytic functions, which does not require taking limits. By applying this formula to certain functions we have found an interesting arithmetic triangle for which we give a recurrence formula. We then explore the links between these numbers, Pascal’s triangle, and Bernoulli’s numbers, for which we obtain a new explicit formula. Furthermore, we present power series and asymptotic expansions of some elementary and special functions, and some links to the Online Encyclopedia of Integer Sequences (OEIS).


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