Reciprocal Hyperbolic Series of Ramanujan Type
Abstract
:1. Introduction
2. Some Lemmas and Transformations
2.1. Three Lemmas
2.2. Three Transformations
3. Evaluations of Some Reciprocal Hyperbolic Series
3.1. Some Preliminary Results
3.2. Evaluations of
3.3. Evaluations of
3.4. Three Differential Equations
4. Examples and Further Results
4.1. Examples
4.2. Further Results
5. Concluding Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Xu, C.; Zhao, J. Reciprocal Hyperbolic Series of Ramanujan Type. Mathematics 2024, 12, 2974. https://doi.org/10.3390/math12192974
Xu C, Zhao J. Reciprocal Hyperbolic Series of Ramanujan Type. Mathematics. 2024; 12(19):2974. https://doi.org/10.3390/math12192974
Chicago/Turabian StyleXu, Ce, and Jianqiang Zhao. 2024. "Reciprocal Hyperbolic Series of Ramanujan Type" Mathematics 12, no. 19: 2974. https://doi.org/10.3390/math12192974
APA StyleXu, C., & Zhao, J. (2024). Reciprocal Hyperbolic Series of Ramanujan Type. Mathematics, 12(19), 2974. https://doi.org/10.3390/math12192974