Advances and Applications in Discrete Mathematics
Volume 22, Issue 2, Pages 153 - 159
(November 2019) http://dx.doi.org/10.17654/ |
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AN ANALYTIC EXACT FORM OF HEAVISIDE STEP FUNCTION
J. Venetis
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Abstract: In this paper, the author obtains an analytic exact form of Heaviside step function, which is also known as Unit Step function and constitutes a fundamental concept of Operational Calculus.
In particular, 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 pointwise 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. |
Keywords and phrases: Heaviside function, single valued function, real variable, integer part.
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