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CERTAIN INTEGRAL REPRESENTATIONS FOR THE RIEMANN ZETA FUNCTION ζ(s) AT POSITIVE INTEGER ARGUMENT

Choi, Junesang

  • Received : 2013.07.26
  • Accepted : 2013.08.22
  • Published : 2013.12.25

Abstract

We aim at presenting certain integral representations for the Riemann Zeta function ${\zeta}(s)$ at positive integer arguments by using some known integral representations of log ${\Gamma}(1+z)$ and ${\psi}(1+z)$.

Keywords

Gamma function;Riemann Zeta function;Hurwitz (or generalized) Zeta function;Psi (or Digamma) function;Polygamma functions;Euler-Mascheroni constant;Fa$\grave{a}$ di Bruno formula

References

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  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.