Series Representation of Power Function
Résumé
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 2 exponential function's $Exp(x), \ x \in \mathbb{N}$ representation is shown and relation between Pascal's triangle and hypercubes is shown in Section 3.
Mots clés
Exponentiation
Mathematical Series
Series Expansion
Derivative
Series representation
Cube (Algebra)
Perfect cube
Hypercube
Binomial distribution
Discrete Mathematics
Applied Mathematics
Preprint
Monomial
Polynomial
Power function
Power series (mathematics)
Power (mathematics)
Exponential function
Divided difference
Diophantine equations
Pascal's triangle
Ordinary differential equation
Forward Finite Difference
Backward Finite Difference
Partial differential equation
Multinomial coefficient
High order finite difference
Partial derivative
Calculus of variations
High order derivative
Partial difference
Differential calculus
Binomial coefficient
Central Finite difference
Difference Equations
Differentiation
Finite differences
Binomial Series
Pascal’s triangle
Newton's interpolation formula
Numerical Differentiation
Pascal triangle
Multinomial theorem
Binomial theorem
Binomial expansion
Calculus
Differential equations
Number theory
Newton's Binomial Theorem
Binomial Sum
Numerical analysis
Mathematics
Mathematical analysis
Functional analysis
Finite difference
Numercal methods
Series
Fichier principal
1603.02468v5.pdf (213.14 Ko)
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SERIES REPRESENTATION REVISED.pdf (208.91 Ko)
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