Impossibility of convergence of a Heun function on the boundary of the disc of convergence

2020/02/05 by Yoon-Seok Choun, Choun, Yoon-Seok
Physics and Astronomy · #30B10 #30B30 #40A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2002.01971

openalex publication_date 2020/02/05 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

The Heun's equation is the Fuchsian equation of second order with four regular singularities. Heun functions generalize well-known special functions such as Spheroidal Wave, Lamé, Mathieu, hypergeometric-type functions, etc. The recursive relation of coefficients starts to appear by putting a power series into the Heun equation. A local Heun function consists of the three term recurrence relation in its power series, and we prove that the function is not convergent on the boundary of the disc of convergence.

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