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