  Looking forward to introducing an analysis in Galois Fields, discrete
functions are considered (such as transcendental ones) and MacLaurin series are
derived by Lagrange's Interpolation. A new derivative over finite fields is
defined which is based on the Hasse Derivative and is referred to as negacyclic
Hasse derivative. Finite field Taylor series and alpha-adic expansions over
GF(p), p prime, are then considered. Applications to exponential and
trigonometric functions are presented. Theses tools can be useful in areas such
as coding theory and digital signal processing.
