Ali Bagheri-Bardi

First, a history of the genesis of Bernoulli numbers is presented. They appear in Taylor expansions of some well-known functions, like Zeta­ Riemann function. Applying Bernoulli polynomial, an extension of Bernoulli numbers, the Euler ­Maclaren formula is proven. Using this formula three applications are given. It is still unknown whether the Euler number is rational or irrational number. Many efforts of experts are concerned with finding sequences that tend to Euler number faster. We have a comprehensive discussion to give such a sequence. Finally, a formula is a given for Euler number.