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New Analytical Functions - Mathematica Verified

Abstract: An attempt was made to analytically describe some basic
functions which are provided with the libraries of mathematical
functions of programming languages. This study will rely on Mathematica
in calculating all numerical results. This study provides global
methods to calculate some discrete functions, which were previously
calculated by using low-level language techniques to chop digits. Using
these definitions we can simulate digital signals without the need for
IF statements and conditions.

A comparison were made between the formulas provided by this study and
some functions provided by Mathematica such as FractionalPart function
that converges very slowly or does NOT converge at all to correct
results. The formulas derived herein were applied to complex numbers
and some interesting results were obtained, such as the integer part of
a complex number equals the Floor of its real part, and will be without
imaginary part, i.e. the integer part of a complex number is a real

Mohamed Al-Dabbagh

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