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.


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.


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