Semicommuting and Commuting Operators for the Heun Family

D. Batic, D. Mills, M. Nowakowski

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageBritish English
Pages (from-to)494-512
Number of pages19
JournalTheoretical and Mathematical Physics(Russian Federation)
Issue number1
StatePublished - 1 Apr 2018


  • biconfluent Heun equation
  • commuting operator
  • confluent Heun equation
  • double confluent Heun equation
  • factorization
  • generalized Heun equation
  • Heun equation
  • semicommuting operator
  • triconfluent Heun equation


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