Approximation for the gamma function via the tri-gamma function

Abstract

Abstract In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.

Keywords

• approximation
• gamma function
• inequalities
• multiple-correction method