Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis
Abstract
Split-complex numbers $\mathbb{R}^{1,1}$ are an extension of the real numbers $\mathbb{R}$, forming a commutative ring generated by two real numbers and featuring two zero divisors. By utilizing the properties of split-complex numbers, this paper mainly presents criteria for the convergence of series with positive terms in split-complex analysis, including proofs of the comparison criterion, the D'Alembert criterion, the Cauchy criterion, the Cauchy-Hadamard criterion, and the Raabe criterion on $\mathbb{R}^{1,1+} \setminus \{0\}$. The results demonstrate that the general criteria for series with positive terms in real analysis are still applicable in split-complex analysis. The results obtained further refine the theoretical framework of split-complex numbers.
Keywords
References
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Details
Primary Language
English
Subjects
Pure Mathematics (Other)
Journal Section
Research Article
Authors
Publication Date
December 31, 2025
Submission Date
August 12, 2025
Acceptance Date
November 9, 2025
Published in Issue
Year 2025 Number: 53
APA
Huang, Z., Peng, L., & Gu, Y. (2025). Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis. Journal of New Theory, 53, 24-35. https://doi.org/10.53570/jnt.1763538
AMA
1.Huang Z, Peng L, Gu Y. Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis. JNT. 2025;(53):24-35. doi:10.53570/jnt.1763538
Chicago
Huang, Zhishang, Liudi Peng, and Yongyi Gu. 2025. “Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis”. Journal of New Theory, nos. 53: 24-35. https://doi.org/10.53570/jnt.1763538.
EndNote
Huang Z, Peng L, Gu Y (December 1, 2025) Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis. Journal of New Theory 53 24–35.
IEEE
[1]Z. Huang, L. Peng, and Y. Gu, “Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis”, JNT, no. 53, pp. 24–35, Dec. 2025, doi: 10.53570/jnt.1763538.
ISNAD
Huang, Zhishang - Peng, Liudi - Gu, Yongyi. “Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis”. Journal of New Theory. 53 (December 1, 2025): 24-35. https://doi.org/10.53570/jnt.1763538.
JAMA
1.Huang Z, Peng L, Gu Y. Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis. JNT. 2025;:24–35.
MLA
Huang, Zhishang, et al. “Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis”. Journal of New Theory, no. 53, Dec. 2025, pp. 24-35, doi:10.53570/jnt.1763538.
Vancouver
1.Zhishang Huang, Liudi Peng, Yongyi Gu. Study on the Convergence and Divergence of Positive Series in Split-Complex Analysis. JNT. 2025 Dec. 1;(53):24-35. doi:10.53570/jnt.1763538