On some complete monotonic functions
Mohamed Bouali
TL;DR
This paper investigates complete monotonic functions, confirming some conjectures and disproving others, motivated by previous open questions related to inequalities involving the gamma and trigamma functions.
Contribution
It provides new proofs and counterexamples concerning the complete monotonicity of functions linked to gamma and trigamma functions, advancing understanding in this mathematical area.
Findings
Confirmed certain conjectures on complete monotonicity.
Disproved some previously open questions.
Enhanced understanding of inequalities involving special functions.
Abstract
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function",we confirm among other results and disprove other one.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results