Open AccessA note on characteristic function for Bernstein polynomials involving special numbers and polynomials
Author(s) -
Buket Şimşek
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2002543s
Subject(s) - mathematics , difference polynomials , bernstein polynomial , discrete orthogonal polynomials , classical orthogonal polynomials , wilson polynomials , hahn polynomials , generating function , stirling number , bernoulli polynomials , stirling numbers of the second kind , orthogonal polynomials , macdonald polynomials , gegenbauer polynomials , pure mathematics , bernoulli number , order (exchange) , bell polynomials , recurrence relation , discrete mathematics , combinatorics , finance , economics
The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.