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Research Article | Open Access

Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

H. C. Vidya1, B. A. Rao2( )
Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, Karnataka, India
Computer Science and Engineering Department, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, Karnataka, India
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Abstract

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical η-functions and h-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and h-functions, thereby establishing links between class one infinite series and h-functions.

Keywords

Eisenstein seriesDedekind η-functionclass one infinite seriesdifferential equations
CLC number: 11F20, 11M36, 34K60

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 28955-28969
DOI: 10.3934/math.20241405

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Vidya HC, Rao BA. Utilization of Ramanujan-type Eisenstein series in the generation of differential equations. AIMS Mathematics, 2024, 9(10): 28955-28969. https://doi.org/10.3934/math.20241405

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Received: 06 July 2024
Revised: 06 September 2024
Accepted: 12 September 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)