New Generalization of Eulerian polynomials and their applications
Number Theory
2019-07-04 v3
Abstract
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic Numbers. Also, we give relations between Eulerian polynomials with a and b parameters, Bernstein polynomials, Poly-logarithm function, Bernoulli numbers and Euler numbers. Moreover, we see that our polynomials at a =-1 are related to Euler-Zeta function at negative inetegers. Finally, we get Witt's formula for new generalization of Eulerian polynomials which we express in this paper.
Cite
@article{arxiv.1208.1271,
title = {New Generalization of Eulerian polynomials and their applications},
author = {Serkan Araci and Mehmet Acikgoz and Erdoğan Şen},
journal= {arXiv preprint arXiv:1208.1271},
year = {2019}
}
Comments
10 pages, submitted