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Article

Redheffer-Type Bounds of Special Functions

by
Reem Alzahrani
and
Saiful R. Mondal
*,†
Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2023, 11(2), 379; https://doi.org/10.3390/math11020379
Submission received: 30 November 2022 / Revised: 4 January 2023 / Accepted: 8 January 2023 / Published: 11 January 2023

Abstract

In this paper, we aim to construct inequalities of the Redheffer type for certain functions defined by the infinite product involving the zeroes of these functions. The key tools used in our proofs are classical results on the monotonicity of the ratio of differentiable functions. The results are proved using the nth positive zero, denoted by bn(ν). Special cases lead to several examples involving special functions, namely, Bessel, Struve, and Hurwitz functions, as well as several other trigonometric functions.
Keywords: Redheffer inequality; Bessel functions; Struve functions; Dini functions; Lommel functions; q-Bessel functions Redheffer inequality; Bessel functions; Struve functions; Dini functions; Lommel functions; q-Bessel functions

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MDPI and ACS Style

Alzahrani, R.; Mondal, S.R. Redheffer-Type Bounds of Special Functions. Mathematics 2023, 11, 379. https://doi.org/10.3390/math11020379

AMA Style

Alzahrani R, Mondal SR. Redheffer-Type Bounds of Special Functions. Mathematics. 2023; 11(2):379. https://doi.org/10.3390/math11020379

Chicago/Turabian Style

Alzahrani, Reem, and Saiful R. Mondal. 2023. "Redheffer-Type Bounds of Special Functions" Mathematics 11, no. 2: 379. https://doi.org/10.3390/math11020379

APA Style

Alzahrani, R., & Mondal, S. R. (2023). Redheffer-Type Bounds of Special Functions. Mathematics, 11(2), 379. https://doi.org/10.3390/math11020379

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