Convergence Properties of the Perplex Series

Authors

  • Jing Zhang
  • Xixuan Huang

DOI:

https://doi.org/10.54097/d0226f18

Keywords:

Perplex numbers, Convergence, Geometric perplex series.

Abstract

Perplex numbers is a number system similar to the complex numbers. The perplex numbers is a commutative ring with zero divisors. The purpose of this article is to determine convergence properties of the perplex series and to give the geometric series in . Also, we analyze the convergence properties of the geometric perplex series. The properties we show will provide a theoretical basis for its application. The geometric perplex series will be paid more attention in the future and may be used widely in physics.

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References

Robert D. Poodiack, Kevin J. LeClair. Fundamental Theorems of Algebra for the perplexes [J]. The College Mathematics Journal, 2009, 40(5), 322-336.

Ronni Geraldo Gomes de Amorim, Wytler Cordeiro dos Santos, Lindomar Bonfim Carvalho, Ian Rodrigues Massa. A physical approach of perplex numbers [J]. Science Citation Index, 2018.

Vance Blankers, Tristan Rendfrey, Aaron Shukert, Patrick D. Shipman. Julia and Mandelbrot Sets for Dynamics over the Hyperbolic Numbers [J]. Multidisciplinary Digital Publishing Institute, 2019, 3(1), 6.

Simone Fattorini. A simple method to fit geometric series and broken stick models in community ecology and island biogeography [J]. ScienceDirect OnSite, 2005, Volume 28, Issue 3, Pages 199-205.

Chinnaraji Annamalai. Computational Geometric Series Model with Key Applications in Informatics [J]. International Journal of Computational Intelligence Research, 2009, Volume 5, pp. 485-499.

M.L Glasser, C Cosgrove. A Gaussian-geometric finite sum formula [J]. Journal of Mathematical Analysis and Applications, 1989, Volume 142, Issue 2, Pages 331-336.

Roberto B. Corcino, Cristina B. Corcino. An Explicit Formula for Generalized Arithmetic-Geometric Sum [J]. Applied Mathematical Sciences, 2015, Vol. 9, no.114, 5687-5696.

J. Neunhauserer. Geometric Series with randomly increasing exponents [J]. Archiv der Mathematik, 2014, 102, 283-291.

Roger W. Brockett. Volterra series and geometric control theory [J]. Automatica, 1976, Volume12, Issue 2, Pages 167-176.

Howard Sporn. Pythagorean Triples, Complex Numbers, and Perplex Numbers [J]. The College Mathematics Journal, 2017, 48(2), 115-122.

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Published

29-03-2024