The radius of convergence of the Lam\'{e} function
Yoon-Seok Choun
TL;DR
This paper investigates the convergence properties of Lamé functions, explaining why the Poincaré-Perron theorem does not apply to their associated differential equations.
Contribution
It clarifies the limitations of the Poincaré-Perron theorem in analyzing the convergence of Lamé functions.
Findings
Identifies the inapplicability of Poincaré-Perron theorem to Lamé equations
Provides insights into the convergence radius of Lamé functions
Enhances understanding of special function differential equations
Abstract
We consider the radius of convergence of a Lam\'{e} function, and we show why Poincar\'{e}-Perron theorem is not applicable to the Lam\'{e} equation.
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Taxonomy
TopicsFractional Differential Equations Solutions · Advanced Differential Equations and Dynamical Systems · Mathematical functions and polynomials