Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

An Analytic Exact form of Heaviside Function

Version 1 : Received: 17 July 2019 / Approved: 18 July 2019 / Online: 18 July 2019 (14:34:55 CEST)

How to cite: Venetis, J. An Analytic Exact form of Heaviside Function. Preprints 2019, 2019070218. Venetis, J. An Analytic Exact form of Heaviside Function. Preprints 2019, 2019070218.


In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula 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. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.


Heaviside function, single valued function, real variable, integer part


Computer Science and Mathematics, Applied Mathematics

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