2014/05/27 by Plamen Fiziev, Fiziev, Plamen P
Chemistry · Physics and Astronomy · #11B37 #34A25 #34B30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1405.6837
openalex publication_date 2014/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present article we introduce and study a novel type of solutions of the general Heun's equation. Our approach is based on the symmetric form of the Heun's differential equation yielded by development of the Felix Klein symmetric form of the Fuchsian equations with an arbitrary number N≥ 4 of regular singular points. We derive the symmetry group of these equations which turns to be a proper extension of the Mobius group. We also introduce and study new series solution of symmetric form of the general Heun's differential equation (N=4) which treats simultaneously and on an equal footing all singular points. Hopefully, this new form will simplify the resolution of the existing open problems in the theory of general Heun's functions and can be used for development of new effective computational methods.