Completely monotonic functions involving Bateman’s G−function

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Keywords:

Bateman’s G−function, completely monotonic, best possible constant, Bernoulli numbers, Wallis ratio, hyperbolic tangent function.

Abstract

n this paper, we prove the complete monotonicity of some functions involving Bateman’s G−function and show that mceclip0-feefa64dd5f37439c6fbfdbe9c692a2f.png where α = 1 and β = 0 are the best possible constants, which is a refinement of a recent result. Then, we give a new proof of Slavi´c inequality about Wallis ratio Wm and provide a new inequality for Wm. Our new inequality improves some recent related works. We also present two inequalities for the hyperbolic tangent function.

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Published

2021-10-16

How to Cite

Mansour Mahmoud, Ahmed Talat, Hesham Moustafa, & Ravi P. Agarwal. (2021). Completely monotonic functions involving Bateman’s G−function. Journal of Computational Analysis and Applications (JoCAAA), 29(5), 970–986. Retrieved from http://eudoxuspress.com/index.php/pub/article/view/207

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