Redheffer-Type Bounds of Special Functions

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 pr...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-01, Vol.11 (2), p.379
Main Authors: Alzahrani, Reem, Mondal, Saiful R.
Format: Article
Language:English
Subjects:
Bessel functions
Dini functions
Inequality
Lommel functions
q-Bessel functions
Redheffer inequality
Struve functions
Trigonometric functions
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11020379