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AN EXACT FORM OF SIGNUM FUNCTION
Keywords:
signum function, singularity function, inverse trigonometric functions, finite summationDOI:
https://doi.org/10.17654/0974165824022Abstract
In this paper, we derive an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication and Control Theory along with Digital Control Systems and is also involved in many other fields of applied mathematics and engineering.
In particular, this important function is exhibited in a simple manner as a finite combination of five inverse tangent functions. The novelty of this work when compared to other analytical expressions of this function is that the proposed explicit representation is not performed in terms of miscellaneous special functions, such as Bessel functions, Error function, and Beta function, and also is neither the limit of a function, nor the limit of a sequence of functions with a point-wise or uniform convergence.
Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Control Theory techniques and other engineering practices.
Received: March 21, 2024
Accepted: April 24, 2024
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