A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials

By Serkan Araci, Mehmet Acikgoz. 2012

152 citations recorded by the source corpus.

The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of Bernstein polynomials and Frobenius-Euler numbers and polynomials. To be more precise we summarize our results as follows, we obtain some combinatorial relations between Frobenius-Euler numbers and polynomials. Furthermore, we derive an integral representation of Bernstein polynomials of degree n on Zp . Also we deduce a fermionic p-adic integral representation of product Bernstein polynomials of different degrees n1, n2,...on Zp and show that it can be written with Frobenius-Euler numbers which yields a deeper insight into the effectiveness of this type of generalizations. Our applications possess a number of interesting properties which we state in this paper.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/80d6da8f144f7b66fed6ddcaae240bd5fccb91ec