Integral Representations for the Euler-Mascheroni Constant γ

Abstract

Since the time of Euler, the so-called Euler-Mascheroni constant γ has been involved in a wide variety of important mathematical formulas and results. Among these formulas and results, a considerably large number of integral representations of γ have been developed. Here we aim at investigating several further integral expressions for the Euler-Mascheroni constant γ.

Keywords:

• Euler-Mascheroni constant
• Gamma function
• Psi (or Digamma) function
• Riemann Zeta function
• Hurwitz (or generalized) Zeta function
• Bernoulli numbers
• Bernoulli polynomials
• Harmonic numbers
• Residue calculus

2000 Mathematics Subject Classification :

• Primary: 11M06
• 33B99
• Secondary: 33C05