The Asymptotic Expansion for a Class of Convergent Sequences Defined by Integrals

Dorin Andrica () and Dan Ştefan Marinescu
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Dorin Andrica: Babeş-Bolyai University
Dan Ştefan Marinescu: Iancu de Hunedoara National College

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 35-52 from Springer

Abstract: Abstract We obtain the complete asymptotic expansion of the sequence defined by ∫ 0 1 f ( x ) g ( x n ) d x $$\int _0^1f(x)g(x^n)dx$$ , where the functions f and g satisfy various conditions. The main result is applied in Sect. 4 to find the complete asymptotic expansion of some classical sequences.

Keywords: Bounded convergence theorem; Riemann integrable function; Lebesgue integrability criterion; Asymptotic convergence order; Asymptotic expansion; Primary 26A42; Secondary 28A20 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_3

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DOI: 10.1007/978-3-030-84122-5_3

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