arXiv (Cornell University)· 2012· Preprint
A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
- 150citations
- 2012year
Short summary
New combinatorial relations and integral representations link Frobenius-Euler numbers/polynomials with Bernstein polynomials on Zp.
AI-generated from the title and abstract; the full text is not read.
Key points
- Derives combinatorial relations between Frobenius-Euler numbers and polynomials.
- Obtains an integral representation for Bernstein polynomials of degree n on Zp.
- Deduces a fermionic p-adic integral representation for products of Bernstein polynomials of different degrees.
- Shows that these product representations can be expressed using Frobenius-Euler numbers.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. arXiv (Cornell University), 2012 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics