Series Representation of Power Function

Kolosov Petro (1)

1 Odessa National I.I.Mechnikov University

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, except above described theorems.

Mots clés: Number to power; Cube number; Series representation; Series expansion; Binomial theorem; Power function

Domaines: Théorie des nombres [math.NT]

Kolosov Petro. Series Representation of Power Function. 2016. ⟨hal-01283042v1⟩