# Euler Numbers

## Euler Numbers

in mathematics, the integers *E*_{n} that are the coefficients of *t ^{n}*/

*n*! in the expansion of the function 1/cosh

*t*in the power series

These numbers, which were introduced by L. Euler in 1755, are related by the formula (*E* + 1)^{n} + (*E* – 1)^{n} = 0, *n* = 1, 2, 3, . . ., *E*_{0} = 1 (after raising to the power, *E*_{k} must be inserted for *E*^{k}). The following relations hold between Euler numbers and Bernoulli numbers:

Euler numbers are encountered in various formulas of mathematical analysis.