Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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NOTE ON CAHEN′S INTEGRAL FORMULAS

  • Choi, June-Sang (Department of Mathematics, College of Natural Sciences, Dongguk University)
  • Published : 2002.01.01
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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.

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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. Complex Variables and Applications (2nd Ed.) R. V. Churchill
  3. Higher Transcendental Functions v.I A. Erdelyi;W. Magnus, F.;Oberhettinger;F. G. Tricomi
  4. Table of Integrals, Series, and Products I. S. Gradshteyn;I. M. Ryzhik
  5. A Course of Modern Analysis (4th Ed.) E. T. Whittaker;G. N. Watson