Article
Version 3
Preserved in Portico This version is not peer-reviewed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)
Version 6 : Received: 16 August 2018 / Approved: 17 August 2018 / Online: 17 August 2018 (11:10:47 CEST)
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)
Version 6 : Received: 16 August 2018 / Approved: 17 August 2018 / Online: 17 August 2018 (11:10:47 CEST)
How to cite: Kolosov, P. Series Representation of Power Function. Preprints 2017, 2017110157. https://doi.org/10.20944/preprints201711.0157.v3 Kolosov, P. Series Representation of Power Function. Preprints 2017, 2017110157. https://doi.org/10.20944/preprints201711.0157.v3
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
https://goo.gl/t22zuk: Matchematica codes of most formulas - .txt format
https://goo.gl/8NN1Zy: Mathematica computable file - .cdf format
https://oeis.org/A287326: OEIS sequence related to Triangle (1.17)
https://kolosovpetro.github.io/: Related preprints
Keywords
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
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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