Double Inequalities for Complete Monotonicity Degrees of Remainders of Asymptotic Expansions of the Gamma and Digamma Functions

TL;DR

This paper confirms conjectures regarding the completely monotonic degrees of remainders in the asymptotic expansions of the gamma and digamma functions, providing new bounds and inequalities.

Contribution

It proves conjectures on the monotonic degrees of remainders and establishes bounds for these degrees in the context of gamma and digamma functions.

Findings

Confirmed conjectures on monotonic degrees

Derived bounds for these degrees

Enhanced understanding of asymptotic remainders

Abstract

Motivated by several conjectures posed in the paper " Completely monotonic degrees for a difference between the logarithmic and psi functions",we confirm in this work some conjectures on completely monotonic degrees of remainders of the asymptotic expansion of the logarithm of the gamma function and the digamma function and we give two bounded for this degrees.