Sharp bounds for gamma and digamma function arising from Burnside's formula

Abstract

The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and digamma function.

Keywords

• factorial \(n\)
• Stirling's formula
• Burnside's formula
• complete monotonicity
• Euler-Mascheroni constant
• sharp inequalities