On the link between finite difference and derivative of polynomials

Abstract : The main aim of this paper to establish the relations between forward, backward and central finite (divided) differences (that is discrete analog of the derivative) and partial & ordinary high-order derivatives of the polynomials.
Keywords : Pascal triangle Binomial expansion Newton's interpolation formula Binomial theorem Binomial Series Pascal’s triangle Newton's Binomial Theorem Binomial coefficient Central Finite difference Backward Finite Difference Forward Finite Difference Finite difference coefficient Numerical Differentiation Difference Equations High order derivative Differential calculus Calculus Differential equations Differentiation Derivatives Finite differences Partial difference Partial derivative Partial differential equation Ordinary differential equation High order finite difference Divided difference Derivative Finite difference Diophantine equations Perfect cube Euler number Cube (Algebra) Mathematical Series Power (mathematics) Exponentiation Exponential function Power series (mathematics) Monomial Polynomial Power function Multinomial theorem Binomial Sum Mathematics Math Maths Science Algebra Number theory Numerical analysis Mathematical analysis Functional analysis STEM Numercal methods Classical Analysis and ODEs Analysis of PDEs General Mathematics Discrete Mathematics Applied Mathematics Calculus of variations q-derivative 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
13 pages, 1 figure, arXiv:1608.00801, DOI: 10.6084/m9.figshare.4955384 2017
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Kolosov Petro. On the link between finite difference and derivative of polynomials. 13 pages, 1 figure, arXiv:1608.00801, DOI: 10.6084/m9.figshare.4955384 2017. 〈hal-01350976v4〉

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