# 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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https://hal.archives-ouvertes.fr/hal-01283042
Contributor : Petro Kolosov <>
Submitted on : Saturday, May 6, 2017 - 5:26:32 PM
Last modification on : Thursday, August 15, 2019 - 3:40:02 PM
Long-term archiving on : Monday, August 7, 2017 - 12:21:43 PM

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Kolosov Petro. Series Representation of Power Function. 2017. ⟨hal-01283042v5⟩

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