Some identities involving Bernoulli numbers and Euler numbers.

From: Scientia Magna | Date: January 1, 2006| Author: | Copyright information

Abstract The main purpose of this paper is using the elementary method to obtain some interesting identities involving the Bernoulli numbers and the Euler numbers.

Keywords The Bernoulli and the Euler numbers; Identity; Elementary method.

[section] 1. Introduction

Let z be any complex number with |z|

z/[e.sup.z] - 1 = [[infinity] summation over (n=0)] [B.sub.n][z.sup.n]/n!, |z|

and

1/cos z = [[infinity] summation over (n=0)] [E.sub.2n][[z.sup.2n]/(2n)!. (2)

For example, [B.sub.0] = 1, [B.sub.1] = -1/2, [B.sub.2] = -1/6, [B.sub.4] = -1/30, [B.sub.6] = 1/42, ...

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