## 17. Introducing An Analysis in Finite Fields

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.

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