On an arithmetic triangle of numbers arising from inverses of analytic functions.

Bagdasaryan, Armen G.; Bagdasar, Ovidiu

dc.contributor.author	Bagdasaryan, Armen G.
dc.contributor.author	Bagdasar, Ovidiu
dc.date.accessioned	2018-12-17T14:29:53Z
dc.date.available	2018-12-17T14:29:53Z
dc.date.issued	2018-12-06
dc.identifier.citation	Bagdasaryan, 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.2018.11.003	en
dc.identifier.issn	1571-0653
dc.identifier.doi	10.1016/j.endm.2018.11.003
dc.identifier.uri	http://hdl.handle.net/10545/623233
dc.description.abstract	The 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.sponsorship	O. 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.iso	en	en
dc.publisher	Elsevier	en
dc.relation.ispartofseries	Proceedings of TCDM'18	en
dc.relation.url	https://linkinghub.elsevier.com/retrieve/pii/S1571065318301987	en
dc.rights	Archived with thanks to Electronic Notes in Discrete Mathematics	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	*
dc.subject	Inversion formula	en
dc.subject	Analytic functions	en
dc.subject	Arithmetic triangle	en
dc.subject	Recurrent sequences	en
dc.subject	Bernoulli numbers	en
dc.subject	Integer sequences	en
dc.title	On an arithmetic triangle of numbers arising from inverses of analytic functions.	en
dc.type	Article	en
dc.contributor.department	American University of the Middle East	en
dc.contributor.department	University of Derby	en
dc.identifier.journal	Electronic Notes in Discrete Mathematics	en
html.description.abstract	The 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).