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

2020/02/07 by Yoon-Seok Choun, Choun, Yoon-Seok
Mathematics · #30B10 #30B30 #40A05 #Algebraic and Geometric Analysis #Applied mathematics #Boundary (topology) #Classical Analysis and ODEs (math.CA) #Convergence (economics) #Economics #FOS: Mathematics #Function (biology) #Impossibility #Mathematical analysis #Mathematics #Political science #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2002.08170

openalex publication_date 2020/02/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The confluent Heun equation is one of 4 confluent forms of Heun's differential equation in which is the Fuchsian equation of second order with four regular singularities. A confluent Heun function is applicable to diverse areas such as theory of rotating/non-rotating black hole, the gauge theories on thick brane words, Schrodinger equation for hydrogen molecule ion in Stark effect and etc. The confluent Heun function consists of the three term recurrence relation in its power series, and we show that the function is divergent on the boundary of the disc of convergence.

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