The Relationships Between the Bernoulli Numbers B2n & an And the Euler Numbers E2n & bn

  • Mohammed R. Karim Department of Mathematics, Alabama A&M University, Normal, AL 35762, USA
Keywords: Riemann zeta function, Bernoulli numbers, Euler numbers, Sum of Series.

Abstract

Traditionally, the values of Riemann zeta function at the even positive integers have been formulated in terms of Bernoulli numbers n B2 and the sums of the alternating series of odd powers of the reciprocal of odd positive integers have been calculated in terms of Euler numbers . 2n E However, the present author reproduced the sum of the same series using different procedures in terms of two rational numbers n a and . n b In this paper, the relationships between n B2 & n a and n E2 & n b have been established. Consequently, some of the theorems and corollaries in [5] have been restated in terms of n B2 and E2n.

Published
2017-06-10
Section
Articles