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TMF, 2018, Volume 195, Number 1, Pages 6–26 (Mi tmf9367)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

DOI: https://doi.org/10.4213/tmf9367

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

Bibliographic databases:

Document Type: Article
PACS: 33E99, 34A05, 34A30
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Hortacsu M., “Heun Functions and Some of Their Applications in Physics”, Adv. High. Energy Phys., 2018, 8621573  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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