Published April 30, 2017 | Version v1
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Series Representation of Power Function

Authors/Creators

  • 1. Independent

Description

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.

MSC 2010: 40C15, 32A05

arXiv:1603.02468

DOI: 10.6084/m9.figshare.3475034

Notes

12 pages, arXiv:1603.02468, DOI: 10.6084/m9.figshare.3475034

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series_representation_of_power_function_2017_kolosov_petro_number_theory_mathematics.pdf

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Additional details

Related works

Is identical to
arXiv:1603.02468 (arXiv)
10.17605/OSF.IO/657QH (DOI)

References

  • Conway, J. H. and Guy, R. K. "Pascal's Triangle." In The Book of Numbers. New York: Springer-Verlag, pp. 68-70, 1996.
  • Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 10, 1972.
  • Weisstein, Eric W. "Power." From MathWorld
  • Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 307-308, 1985.
  • Rudin, Walter (1987). Real and complex analysis (3rd ed.). New York: McGraw-Hill. p. 1. ISBN 978-0-07-054234-1.
  • Weisstein, Eric W. "Finite Difference." From MathWorld
  • Richardson, C. H. An Introduction to the Calculus of Finite Differences. p. 5, 1954.
  • Bakhvalov N. S. Numerical Methods: Analysis, Algebra, Ordinary Differential Equations p. 59, 1977.

Subjects

Mathematics
1
Math
2
Maths
3
Science
4
Algebra
5
Number theory
6
Numerical analysis
7
Mathematical analysis
8
Functional analysis
9
STEM
10
Numercal methods
11
Classical Analysis and ODEs
12
Analysis of PDEs
13
General Mathematics
14
Discrete Mathematics
15
Applied Mathematics
16
Calculus of variations
17