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

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Dorin Andrica

    (Babeş-Bolyai University)

  • Dan Ştefan Marinescu

    (Iancu de Hunedoara National College)

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.

Suggested Citation

  • Dorin Andrica & Dan Ştefan Marinescu, 2022. "The Asymptotic Expansion for a Class of Convergent Sequences Defined by Integrals," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 35-52, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_3
    DOI: 10.1007/978-3-030-84122-5_3
    as

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