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

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Approximation and Computation in Science and Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 180))

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Abstract

We obtain the complete asymptotic expansion of the sequence defined by \(\int _0^1f(x)g(x^n)dx\), 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.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

    Dorin Andrica

  2. Iancu de Hunedoara National College, Hunedoara, Romania

    Dan Ştefan Marinescu

Authors
  1. Dorin Andrica
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  2. Dan Ştefan Marinescu
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Corresponding author

Correspondence to Dorin Andrica .

Editor information

Editors and Affiliations

  1. Department of Maths and Engineering Sciences, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Andrica, D., Marinescu, D.Ş. (2022). The Asymptotic Expansion for a Class of Convergent Sequences Defined by Integrals. In: Daras, N.J., Rassias, T.M. (eds) Approximation and Computation in Science and Engineering. Springer Optimization and Its Applications, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-030-84122-5_3

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