BICOMPLEX AND MULTICOMPLEX GENERALIZATION OF GROWTH PROPERTIES OF ENTIRE SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS
By
Sanjib Kumar Datta
Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist: Nadia, West Bengal, India-741235
Email: sanjibdatta05@gmail.com
(Received: November 03, 2025; In format: February 21, 2021, 2026; revised: June 07, 2026; Accepted June 18, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56102
Abstract
This paper extends several classical results concerning the comparative growth rates of entire solutions of linear differential equations with entire coefficients to the bicomplex and multicomplex settings. After introducing a detailed algebraic and analytic framework, we establish general forms of all lemmas and theorems using independent proofs based on the idempotent representation of bicomplex and multicomplex numbers. Comprehensive examples are also provided in the paper.
2020 Mathematical Sciences Classification: 30D20, 30D15, 30G35, 32A30, 34K41, 34M03, 34M04.
Keywords and Phrases: Entire solution, Bicomplex and multicomplex valued functions, Growth, Idempotent decomposition, Bicomplex and multicomplex differential equations