CERTAIN INTEGRAL REPRESENTATIONS OF GENERALIZED STIELTJES CONSTANTS γ_k(a)

Abstract

Abstract. A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) γ k and the generalized Stieltjes constants γ k (a) have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants γ k (a) by choosing to use four known integral representations for the generalized zeta function ζ(s, a). As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants γ k . Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.