Article ID: MTJPAM-D-23-00034

Title: On the 2-dissection and 4-dissection for Ramanujan-Selberg continued fraction and its reciprocal


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00034; Volume 6 / Issue 3 / Year 2024, Pages 72-82

Document Type: Research Paper

Author(s): ‪Ze-Qian Luo a , Qiu-Ming Luo b

aDepartment of Geography and Tourism, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing 401331, People’s Republic of China

bDepartment of Mathematics, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing 401331, People’s Republic of China

Received: 19 October 2023, Accepted: 27 October 2023, Published: 24 November 2023

Corresponding Author: Qiu-Ming Luo (Email address: luomath2007@163.com)

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Abstract

In this paper, we establish the 2-dissection and 4-dissection for Ramanujan-Selberg continued fraction and its reciprocal. We show an eight-terms expansion of the reciprocal of Ramanujan-Selberg continued fraction. In the end we give some remarks and suggest two open problems and conjectures on the dissections of the Ramanujan-Selberg continued fraction.

Keywords: Ramanujan-Selberg continued fraction, dissection, reciprocal, Jacobi triple product identity, conjecture

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Cite this article

How to cite this article: ‪Z.-Q. Luo and Q.-M. Luo, On the 2-dissection and 4-dissection for Ramanujan-Selberg continued fraction and its reciprocal, Montes Taurus J. Pure Appl. Math. 6 (3), 72-82, 2024; Article ID: MTJPAM-D-23-00034.