Preprint Article Version 2 This version is not peer-reviewed

Series Representation of Power Function

Version 1 : Received: 24 November 2017 / Approved: 24 November 2017 / Online: 24 November 2017 (05:15:26 CET)
Version 2 : Received: 12 January 2018 / Approved: 18 January 2018 / Online: 18 January 2018 (03:37:52 CET)
Version 3 : Received: 18 February 2018 / Approved: 19 February 2018 / Online: 19 February 2018 (16:42:41 CET)
Version 4 : Received: 8 May 2018 / Approved: 9 May 2018 / Online: 9 May 2018 (06:31:05 CEST)
Version 5 : Received: 28 May 2018 / Approved: 28 May 2018 / Online: 28 May 2018 (08:26:14 CEST)

How to cite: Kolosov, P. Series Representation of Power Function. Preprints 2017, 2017110157 (doi: 10.20944/preprints201711.0157.v2). Kolosov, P. Series Representation of Power Function. Preprints 2017, 2017110157 (doi: 10.20944/preprints201711.0157.v2).

Abstract

In this paper described numerical expansion of natural-valued power function xn, in point x = x0 where n, x0 - natural numbers. Apply- ing 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 Bi- nomial sum. Additionally, in section 4 exponential function’s ex representation is shown.

Supplementary and Associated Material

Subject Areas

power function; binomial coefficient; binomial theorem; finite difference; perfect cube; exponential function; pascal’s triangle; series representation; binomial sum; multinomial theorem; multinomial coefficient; binomial distribution

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