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. In Application 3 generalized calculus of finite differences, based on expression (1.9) is shown.

Comments: 13 pages, 5 figures, arXiv:1603.02468, Keywords: Power function, Monomial, Polynomial, Power series, Finite difference, Derivative, Differential calculus, Differentiation, Binomial coefficient, Newton's Binomial Theorem, Exponential function

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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

Unique-IP document downloads: 36 times

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