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

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.

8 pages, submitted

References in corpus (2)

• On the multiple q-Genocchi and Euler numbers
• On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials

Cited by in corpus (7)

• Higher-order Bernoulli, Frobenius-Euler and Euler polynomials
• Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus
• Sheffer sequences of polynomials and their applications
• Apostol-Euler polynomials arising from umbral calculus
• Umbral calculus and special polynomials
• On the associated sequences of special polynomials
• Umbral calculus and Frobenius-Euler polynomials