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 a-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.