Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

An Explicit Form of Heaviside Step Function

Version 1 : Received: 3 June 2021 / Approved: 4 June 2021 / Online: 4 June 2021 (10:35:46 CEST)

How to cite: Venetis, J. An Explicit Form of Heaviside Step Function. Preprints 2021, 2021060132. Venetis, J. An Explicit Form of Heaviside Step Function. Preprints 2021, 2021060132.


In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.


Heaviside function, explicit form, inverse trigonometric functions


Computer Science and Mathematics, Algebra and Number Theory

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