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

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.