Series Representation of Power Function

Abstract : In this paper described numerical expansion of natural-valued power function $x^n$, in point $x=x_0$ where $n, \ x_0$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newton’s Binomial theorem and MacMillan Double Binomial sum. Additionally, in section 4 exponential function’s $e^x$ representation is shown.
Keywords : q-derivative Applied Mathematics Discrete Mathematics Classical Analysis and ODEs Analysis of PDEs General Mathematics Numercal methods Functional analysis STEM Mathematical analysis Number theory Numerical analysis Science Algebra Math Maths Mathematics Newton's Binomial Theorem Calculus Differential equations Binomial Sum Multinomial theorem Binomial expansion Pascal triangle Binomial theorem Newton's interpolation formula Binomial Series Pascal’s triangle Differentiation Derivatives Finite differences Difference Equations Numerical Differentiation Finite difference coefficient Forward Finite Difference Backward Finite Difference Central Finite difference Binomial coefficient Differential calculus High order derivative Partial derivative Partial difference Calculus of variations Partial differential equation High order finite difference Ordinary differential equation Derivative Divided difference Perfect cube Diophantine equations Finite difference Euler number Mathematical Series Cube (Algebra) Exponentiation Exponential function Power (mathematics) Power series (mathematics) Polynomial Power function Monomial Jackson derivative q-calculus h-calculus Quantum calculus q-difference Quantum algebra Qunatum calculus Hypergeometric series Hypergeometric function Time Scale Calculus Power quantum calculus Quantum difference Quantum variatoinal calculus h-difference arXiv Preprint Open science arXiv.org Open access 0000-0002-6544-8880 Series Expansion Taylor's theorem Taylor's formula Taylor's series Taylor's polynomial Analytic function Series representation Polynomial expansion Taylor theorem Taylor formula Taylor series Taylor polynomial Maclaurin Series Petro Kolosov Kolosov Petro Kolosov kolosov_p_1 KolosovP petro-kolosov kolosov-petro petrokolosov kolosov.petro Kolosov_Petro petro.kolosov.9
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Pré-publication, Document de travail
11 pages, 5 figures, major revisions of sections, abstract shortened and detailed, MSC classifica.. 2017
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https://hal.archives-ouvertes.fr/hal-01283042
Contributeur : Petro Kolosov <>
Soumis le : mardi 1 août 2017 - 23:51:40
Dernière modification le : mardi 12 septembre 2017 - 01:02:34

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Kolosov Petro. Series Representation of Power Function. 11 pages, 5 figures, major revisions of sections, abstract shortened and detailed, MSC classifica.. 2017. <hal-01283042v6>

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