They are integers but have no expression for calculating them. Their only are that the numbers with odd index (http://planetmath.org/IndexingSet) are all 0 and that
The Euler number have intimate relation to the Bernoulli numbers. The first Euler numbers with even index are
One can by hand determine Euler numbers by performing the division of 1 by the Taylor series of hyperbolic cosine (cf. Taylor series via division and Taylor series of hyperbolic functions). Since , the division correspondingly gives only terms with plus sign, i.e. it shows the absolute values of the Euler numbers.
The Euler numbers may also be obtained by using the Euler polynomials :
|Date of creation||2014-12-02 17:43:40|
|Last modified on||2014-12-02 17:43:40|
|Last modified by||pahio (2872)|