Bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function

Abstract

In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of asymptotic expansions for the logarithm of the gamma function and for polygamma functions.

Keywords

• completely monotonic degree
• remainder
• asymptotic expansion
• trigamma function
• completely monotonic function
• conjecture
• gamma function
• polygamma function