This article is cited in 3 papers

Semicommuting and commuting operators for the Heun family

D. Batic^a, D. Mills^b, M. Nowakowski<sup>c

a</sup> Khalifa University of Science and Research, Abu Dhabi, United Arab Emirates
^b Department of Mathematics, University of the West Indies, Jamaica
^c Departamento de Fisica, Universidad de los Andes, Bogota, Colombia

Abstract: We derive the most general families of first- and second-order differential operators semicommuting with the Heun class differential operators. Among these families, we classify all the families that commute with the Heun class. In particular, we find that a certain generalized Heun equation commutes with the Heun differential operator, which allows constructing a general solution of a complicated fourth-order linear differential equation with variable coefficients whose solution cannot be obtained using Maple 16.

Keywords: semicommuting operator, commuting operator, Heun equation, confluent Heun equation, biconfluent Heun equation, double confluent Heun equation, triconfluent Heun equation, generalized Heun equation, factorization.

PACS: 33E99, 34A05, 34A30

Received: 07.03.2017
Revised: 16.05.2017

DOI: 10.4213/tmf9367

 English version: Theoretical and Mathematical Physics, 2018, 195:1, 494–512

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