Please use this identifier to cite or link to this item: http://www.repositorio.ufop.br/handle/123456789/5438
Title: Higher order derivatives of trigonometric functions, stirling numbers of the second kind, and zeon algebra.
Authors: Francisco Neto, Antônio
Issue Date: 2014
Citation: FRANCISCO NETO, A. Higher order derivatives of trigonometric functions, stirling numbers of the second kind, and zeon algebra. Journal of Integer Sequences, v. 17, p. 1/14.9.3-9, 2014. Disponível em: <https://cs.uwaterloo.ca/journals/JIS/VOL17/Neto/neto4.pdf>. Acesso em: 09 abr. 2015.
Abstract: In this work we provide a new short proof of closed formulas for the n-th derivative of the cotangent and secant functions using simple operations in the context of the Zeon algebra. Our main ingredients in the proof comprise a representation of the ordinary derivative as an integration over the Zeon algebra, a representation of the Stirling numbers of the second kind as a Berezin integral, and a change of variables formula under Berezin integration. The approach described here is also suitable to give closed expressions for higher order derivatives of tangent, cosecant and all the aforementioned functions hyperbolic analogues.
URI: http://www.repositorio.ufop.br/handle/123456789/5438
ISSN: 15307638
metadata.dc.rights.license: Authors retain the copyright of their submitted papers. Fonte: Journal of Integer Sequences. <https://cs.uwaterloo.ca/journals/JIS/index.html> Acesso em: 23 abr. 2015.
Appears in Collections:DEPRO - Artigos publicados em periódicos

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