Bounds for the generalized Euler-constant function

Abstract

We establish new upper and lower bounds for the generalized Euler-constant function γ(z) for z ∈ (0, 1) in terms of logarithm function, dilogarithm function and Lerch transcendental Φ.

Keywords:

• Euler-constant function
• Euler–Mascheroni constant
• Somos’ quadratic recurrence constant
• dilogarithm function
• Lerch transcendental
• inequalities

2000 Mathematics Subject Classification:

• Primary 11Y60
• 33E20