Oresme Polynomials and Their Derivatives
Gamaliel Cerda-Morales

TL;DR
This paper introduces Oresme polynomials as a generalization of Oresme numbers, explores their identities using matrix methods, and studies their derivatives and relations, extending the classical sequence with new algebraic properties.
Contribution
The paper presents a novel generalization of Oresme numbers through Oresme polynomials, deriving identities and derivative relations using matrix techniques.
Findings
Derived bilinear index-reduction formulas for Oresme polynomials
Introduced natural extensions called $k$-Oresme polynomials
Established convolution relations for derivatives of these polynomials
Abstract
We study the problem of generalization of Oresme numbers with a new sequence of numbers called Oresme polynomials. Moreover, by using the matrix methods for Oresme polynomials, we obtain the identities including the general bilinear index-reduction formula of these numbers. Further, Oresme polynomials that are natural extensions of the -Oresme numbers are introduced and some relations for the derivatives of these polynomials in the form of convolution are proved.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics · Advanced Mathematical Identities
