General Eulerian Numbers and Eulerian Polynomials
Tingyao Xiong, Hung-ping Tsao, Jonathan I. Hall
TL;DR
This paper introduces generalized Eulerian numbers and polynomials based on arithmetic progressions, extending classical properties to a broader mathematical framework.
Contribution
It defines new generalized Eulerian numbers and polynomials and extends their well-known properties to these new forms.
Findings
Extended classical Eulerian properties to generalized forms
Defined Eulerian numbers for arbitrary arithmetic progressions
Established foundational results for generalized Eulerian polynomials
Abstract
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research