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A new class of polynomials associated with Bernstein and beta polynomials
Author(s) -
Simsek Yilmaz
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2825
Subject(s) - mathematics , orthogonal polynomials , difference polynomials , wilson polynomials , discrete orthogonal polynomials , classical orthogonal polynomials , hahn polynomials , macdonald polynomials , gegenbauer polynomials , jacobi polynomials , koornwinder polynomials , pure mathematics , algebra over a field , generating function , discrete mathematics
The purpose of this paper is to define a new class polynomials. Special cases of these polynomials give many famous family of the Bernstein type polynomials and beta polynomials. We also construct generating functions for these polynomials. We investigate some fundamental properties of these functions and polynomials. Using functional equations and generating functions, we derive various identities related to theses polynomials. We also construct interpolation function that interpolates these polynomials at negative integers. Finally, we give a matrix representations of these polynomials. Copyright © 2013 John Wiley & Sons, Ltd.