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CERTAIN INTEGRAL REPRESENTATIONS FOR THE RIEMANN ZETA FUNCTION ζ(s) AT POSITIVE INTEGER ARGUMENT
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.639-645
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.639
 Title & Authors
CERTAIN INTEGRAL REPRESENTATIONS FOR THE RIEMANN ZETA FUNCTION ζ(s) AT POSITIVE INTEGER ARGUMENT
Choi, Junesang;
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 Abstract
We aim at presenting certain integral representations for the Riemann Zeta function at positive integer arguments by using some known integral representations of log and .
 Keywords
Gamma function;Riemann Zeta function;Hurwitz (or generalized) Zeta function;Psi (or Digamma) function;Polygamma functions;Euler-Mascheroni constant;Fa di Bruno formula;
 Language
English
 Cited by
 References
1.
J. Choi and H. M. Srivastava, Integral representations for the Euler-Mascheroni constant ${\gamma}$, Integral Transforms Spec. Funct. 21 (2010), 675-690. crossref(new window)

2.
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Corrected and Enlarged edition prepared by A. Jerey), Academic Press, New York, 1980; Sixth edition, 2000.

3.
W. J. Kaczor and M. T. Nowak, Problems in Mathematical Analysis II, Continuity and Differentiation, American Mathematical Society, 2001.

4.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.