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Butzer, P.L. and Nessel, R.J. (1971) Fourier Analysis and Approximation, Vol. 1. Reviews in Group Representation Theory, Part A (Pure and Applied Mathematics Series, Vol. 7). Academic Press.

has been cited by the following article:

• TITLE: A New Extension of the Riemann-Lebesgue Lemma

  AUTHORS: Na Li, Yongguo Shi, Kelin Li

  KEYWORDS: Riemann-Lebesgue Lemma, Integral Sequence, Asymptotic Expansions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.5, May 28, 2025

  ABSTRACT: The asymptotic behavior for a sequence of integrals ∫ a b f( x )g( nx )dx ,  a,b∈ℝ,  as n→∞, is investigated, where f is continuous differentiable function and g is a continuous and periodic function. The first two terms asymptotic estimates have been given by [D. Andrica, M. Piticari. Intern. Conf. on Theory and Appl. of Math. and Inf. Thessaloniki, Acta Universitatis Apulensis, 2004(8), 26-39.] with some different assumptions. This paper obtains the complete asymptotic expansions. Some examples are provided.