New Bounds for Gurland-Type Ratios in Terms of the Generalized Nielsen's Beta Function

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Published: 2026-07-20
DOI: https://doi.org/10.56947/x7dwnj62
Keywords:
Nielsen's Beta function, Digamma function, Polygamma function, completely monotonic function, bounds

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Hesham Moustafa
Department of Mathematics and Statistics, Fahad Bin Sultan University, College of Sciences and Humanities, P.O. Box 15700 Tabuk, 71454, Saudi Arabia.
Mansour Mahmoud
Mathematics Department, King Abdulaziz University, Faculty of Science, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

We establish new bounds for Gurland-Type Ratios in terms of the generalized Nielsen's beta function βₕ(y). To achieve this, we investigate the complete monotonicity of certain functions involving βₕ(y) and the Gamma function Γ(y). Furthermore, we derive some sharp bounds that are superior to some recent results.

Article Details

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Vol. 23 No. 2 (2026)

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Articles

How to Cite

New Bounds for Gurland-Type Ratios in Terms of the Generalized Nielsen’s Beta Function. (2026). Gulf Journal of Mathematics, 23(2). https://doi.org/10.56947/x7dwnj62