Computing Hankel determinants $H^{(2)}_m$ of Dixon elliptic functions with modulus $\alpha=0$ using Regular C fraction

Authors

  • Rathinavel Silambarasan Department of Information Technology, School of Information Technology and Engineering,\\ Vellore Institute of Technology, Vellore, Tamilnadu, India
  • Fethi Bin Muhammad Belgacem Math & Natural Sciences Dept.,College of Engineering, International University of Science and Technology (IUK), Kuwait.
  • Kottakkaran Sooppy Nisar Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University,\\ Al Kharj, 11942, Alkharj, Kingdom of Saudi Arabia
  • Dumitru Baleanu Department of Mathematics, Cankaya University, 06530 Ankara, Turkey.

Abstract

In this research paper Dixon elliptic functions (DEF) having modulus, $\alpha=0$, $sm^N(x,0)\ :\ N\ge 1\ sm^N(x,0)cm(x,0)$ and $sm^N(x,0)cm(x,0)\ :\ N\ge 0$ are expanded by Regular C fractions and generalized using the Sumudu transform. Then Hankel determinants $H^{(2)}_m$ of DEF are calculated without resort to Maclaurin's series. For this purpose Heliermann correspondence is applied to Regular C Fraction (RCF) coefficients. Higher order results are given using formal notation and compact form. Some known and previous results are proven and numerical examples given to check the validity in light of this paper's new findings.

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Published

2025-05-30

Issue

Vol. 32 No. 2 (2025): Nonlinear Studies (NS)

Section

Articles

License

Copyright (c) 2025 Rathinavel Silambarasan, Fethi Bin Muhammad Belgacem, Kottakkaran Sooppy Nisar, Dumitru Baleanu

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Computing Hankel determinants $H^{(2)}_m$ of Dixon elliptic functions with modulus $\alpha=0$ using Regular C fraction. (2025). Nonlinear Studies, 32(2), 543-562. https://nonlinearstudies.com/index.php/nonlinear/article/view/3917