Mathematics and Statistics Vol. 2(7), pp. 235 - 237
DOI: 10.13189/ms.2014.020702
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An Analytic Exact Form of the Unit Step Function

J. Venetis ^*
Section of Mechanics, Faculty of Applied Mathematics and Physical Sciences, National Technical University of Athens

ABSTRACT

In this paper, the author obtains an analytic exact form of the unit step function, which is also known as Heaviside function and constitutes a fundamental concept of the Operational Calculus. Particularly, this function is equivalently expressed in a closed form as the summation of two inverse trigonometric functions. The novelty of this work is that the exact representation which is proposed here is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Therefore it may be much more appropriate in the computational procedures which are inserted into Operational Calculus techniques.

KEYWORDS
Unit Step Function, Algebraic Representation, Inverse Trigonometric Function

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] J. Venetis , "An Analytic Exact Form of the Unit Step Function," Mathematics and Statistics, Vol. 2, No. 7, pp. 235 - 237, 2014. DOI: 10.13189/ms.2014.020702.

(b). APA Format:
J. Venetis (2014). An Analytic Exact Form of the Unit Step Function. Mathematics and Statistics, 2(7), 235 - 237. DOI: 10.13189/ms.2014.020702.