Open AccessFormulas derived from moment generating functions and Bernstein polynomials
Author(s) -
Buket Şimşek
Publication year - 2019
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm191227036s
Subject(s) - mathematics , bernstein polynomial , generating function , moment generating function , discrete orthogonal polynomials , classical orthogonal polynomials , moment (physics) , orthogonal polynomials , binomial theorem , variable (mathematics) , difference polynomials , pure mathematics , random variable , discrete mathematics , mathematical analysis , statistics , physics , classical mechanics
The purpose of this paper is to provide some identities derived by moment generating functions and characteristics functions. By using functional equations of the generating functions for the combinatorial numbers y1 (m,n,?), defined in [12, p. 8, Theorem 1], we obtain some new formulas for moments of discrete random variable that follows binomial (Newton) distribution with an application of the Bernstein polynomials. Finally, we present partial derivative formulas for moment generating functions which involve derivative formula of the Bernstein polynomials.