On an arithmetic triangle of numbers arising from inverses of analytic functions.
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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).
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.2018.11.003
JournalElectronic Notes in Discrete Mathematics
Series/Report no.Proceedings of TCDM'18
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