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This article is cited in 3 scientific papers (total in 3 papers)
Semicommuting and commuting operators for the Heun family
D. Batica, D. Millsb, M. Nowakowskic a 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.
Received: 07.03.2017 Revised: 16.05.2017
Citation:
D. Batic, D. Mills, M. Nowakowski, “Semicommuting and commuting operators for the Heun family”, TMF, 195:1 (2018), 6–26; Theoret. and Math. Phys., 195:1 (2018), 494–512
Linking options:
https://www.mathnet.ru/eng/tmf9367https://doi.org/10.4213/tmf9367 https://www.mathnet.ru/eng/tmf/v195/i1/p6
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Abstract page: | 354 | Full-text PDF : | 62 | References: | 38 | First page: | 18 |
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