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.