Number Theory


Series Representation of Power Function

Authors: Kolosov Petro

In this paper described numerical expansion of natural-valued power function x^n, in point x=x_0 where (n, x_0) - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newton’s Binomial theorem and MacMillan Double Binomial sum. Additionally, in section 4 exponential function’s e^x representation is shown.

Comments: 15 pages, 5 figures, 1 table, results generalized, references revised, Mathematica codes in Application 1 rearranged, comments are welcome

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Submission history

[v1] 2017-06-09 07:24:09
[v2] 2017-08-01 15:52:40
[v3] 2017-09-07 17:27:09
[v4] 2017-11-23 17:13:00

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