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, 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
Mots clés
- polynomial
- arxiv
- binomial theorem
- divided difference
- derivative
- Math
- Maths
- Pascal triangle
- Euler number
- n-th difference of n-th power
- binomial expansion
- cubic number
- power series
- high order finite difference
- finite difference
- monomial
- power function
- power
- Newton's binomial theorem
- Pascal's triangle
- number theory
- Preprint
- cube
- Exponential function
- binomial coefficient
- series
- Mathematics
- Science
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