New degenerated polynomials arising from non-classical Umbral Calculus
Number Theory
2018-11-07 v1 Combinatorics
Abstract
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present generalizations of some familiar identities and connection between these kinds of Bernoulli, Euler, and Genocchi polynomials. Moreover, we establish a new analogue of the Euler identity for the degenerate Bernoulli numbers.
Cite
@article{arxiv.1811.02342,
title = {New degenerated polynomials arising from non-classical Umbral Calculus},
author = {Orli Herscovici and Toufik Mansour},
journal= {arXiv preprint arXiv:1811.02342},
year = {2018}
}