On the link between finite difference and derivative of polynomials

Kolosov Petro (1)

1 Odessa National I.I.Mechnikov University

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.

Mots clés: Central Finite difference; Binomial coefficient; Finite difference coefficient; Backward Finite Difference; Differential calculus; Finite differences; Partial derivative; Ordinary differential equation; Partial differential equation; High order finite difference; Divided difference; Exponentiation; Power function; Polynomials; Multinomial theorem

Domaines: Mathématiques [math]; Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Combinatoire [math.CO]

Kolosov Petro. On the link between finite difference and derivative of polynomials. 2017. ⟨hal-01350976v4⟩