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http://dx.doi.org/10.7858/eamj.2015.005

CERTAIN INTEGRAL REPRESENTATIONS OF GENERALIZED STIELTJES CONSTANTS γk(a)  

Shin, Jong Moon (Department of Mathematics, Dongguk University)
Publication Information
East Asian mathematical journal / v.31, no.1, 2015 , pp. 41-53 More about this Journal
Abstract
A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.
Keywords
Gamma function; Riemann Zeta function; Hurwitz (or generalized) Zeta function; Psi (or Digamma) function; Polygamma functions; Euler-Mascheroni constant; Stieltjes constants;
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