Certain integral representations of Stieltjes constants γn

Junesang Choi
2013 Journal of Inequalities and Applications  
A remarkably large number of integral formulas for the Euler-Mascheroni constant γ have been presented. The Stieltjes constants (or generalized Euler-Mascheroni constants) γ n and γ 0 = γ , which arise from the coefficients of the Laurent series expansion of the Riemann zeta function ζ (s) at s = 1, have been investigated in various ways, especially for their integral representations. Here we aim at presenting certain integral representations for γ n by choosing to use three known integral
more » ... known integral representations for the Riemann zeta function ζ (s). Our method used here is similar to those in some earlier works, but our results seem a little simpler. Some relevant connections of some special cases of our results presented here with those in earlier works are also pointed out. MSC: Primary 11M06; 11M35; secondary 11Y60; 33B15
doi:10.1186/1029-242x-2013-532 fatcat:zyxgnokimbhq5dil2eao64by4m