The Euler polynomials are certain polynomials of the indeterminate with rational coefficients (whose denominators may only be powers of 2). The Euler polynomials may be defined by means of the generating function such that
i.e. one can get them by dividing the Taylor series by the Taylor series . There are also explicit formulae for the polynomials, e.g.
The first seven Euler polynomials are
The Euler polynomials have the beautiful addition formula
and the derivative
The Euler polynomials form an example of Appell sequences.
|Date of creation||2013-03-22 19:07:07|
|Last modified on||2013-03-22 19:07:07|
|Last modified by||pahio (2872)|