# Series Representation of Power Function

Abstract : 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 2 exponential function's $Exp(x), \ x \in \mathbb{N}$ representation is shown and relation between Pascal's triangle and hypercubes is shown in Section 3.
Keywords :
Type de document :
Pré-publication, Document de travail
19 pages, 9 figures, 2 tables, typos and references are revised, results generalized 2018
Domaine :

Littérature citée [36 références]

https://hal.archives-ouvertes.fr/hal-01283042
Contributeur : Petro Kolosov <>
Soumis le : vendredi 16 février 2018 - 22:23:01
Dernière modification le : vendredi 23 février 2018 - 01:06:06

### Fichier

SERIES REPRESENTATION REVISED ...
Fichiers produits par l'(les) auteur(s)

### Licence

Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Pas de modification 4.0 International License

### Citation

Petro Kolosov. Series Representation of Power Function. 19 pages, 9 figures, 2 tables, typos and references are revised, results generalized 2018. 〈hal-01283042v9〉

### Métriques

Consultations de la notice

## 20

Téléchargements de fichiers