Series Representation of Power Function

Abstract : This paper presents the way to make expansion for the next form function: $y=x^n, \ \forall(x,n) \in {\mathbb{N}}$ to the numerical series. The most widely used methods to solve this problem are Newton’s Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, based on induction from particular to general case, except above described theorems. \ \ \ Keywords: power, power function, monomial, polynomial, power series, third power, series, finite difference, divided difference, high order finite difference, derivative, binomial coefficient, binomial theorem, Newton's binomial theorem, binomial expansion, n-th difference of n-th power, number theory, cubic number, cube, Euler number, exponential function, Pascal triangle, Pascal’s triangle, mathematics, math, maths, science, arxiv, preprint, наука, математика
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Pré-publication, Document de travail
12 pages, arXiv:1603.02468, DOI:10.6084/m9.figshare.3475034 2017
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https://hal.archives-ouvertes.fr/hal-01283042
Contributeur : Petro Kolosov <>
Soumis le : samedi 6 mai 2017 - 17:26:32
Dernière modification le : jeudi 10 août 2017 - 01:01:04
Document(s) archivé(s) le : lundi 7 août 2017 - 12:21:43

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Kolosov Petro. Series Representation of Power Function. 12 pages, arXiv:1603.02468, DOI:10.6084/m9.figshare.3475034 2017. <hal-01283042v5>

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