The Ramanujan Journal

, Volume 4, Issue 4, pp 397–419 | Cite as

A New Method for Investigating Euler Sums

  • Ankur Basu
  • Tom M. Apostol

Abstract

Euler discovered a recursion formula for the Riemann zeta function evaluated at the even integers. He also evaluated special Dirichlet series whose coefficients are the partial sums of the harmonic series. This paper introduces a new method for deducing Euler's formulas as well as a host of new relations, not only for the zeta function but for several allied functions.

Riemann zeta function Euler sums recursion formulas 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Ankur Basu
    • 1
  • Tom M. Apostol
    • 2
  1. 1.West BengalIndia
  2. 2.Department of MathematicsCalifornia Institute of TechnologyPasadena

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