Series Representation of Power Function
Résumé
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
Newton’s binomial theorem
binomial theorem
binomial coefficient
power
power function
power series
series
divided difference
high order finite difference
derivative
binomial expansion
n-th difference of n-th power
cubic number
cube
Euler number
exponential function
Mathematics
Number theory
Pascal’s triangle
Origine : Fichiers produits par l'(les) auteur(s)
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