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NOTE ON CAHEN′S INTEGRAL FORMULAS

Choi, June-Sang

  • Published : 2002.01.01

Abstract

We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

Keywords

Gamma function;Riemann′s ζ-function;Hurwitz Zeta function;Euler numbers

References

  1. Ecole Normale Superieure v.11 no.3 Sur la fonction ?(s) de Riemann et sur des fonctions analoyues, Annales Scientifiques M. E. Cahen
  2. Higher Transcendental Functions v.I A. Erdelyi;W. Magnus, F.;Oberhettinger;F. G. Tricomi
  3. Table of Integrals, Series, and Products I. S. Gradshteyn;I. M. Ryzhik
  4. Complex Variables and Applications (2nd Ed.) R. V. Churchill
  5. A Course of Modern Analysis (4th Ed.) E. T. Whittaker;G. N. Watson