Geodesic
Semicommuting and commuting operators for the~Heun family
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 6-26

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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, generalized Heun equation, factorization.
Mots-clés : Heun equation, confluent Heun equation, biconfluent Heun equation, double confluent Heun equation, triconfluent Heun equation 
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     author = {D. Batic and D. Mills and M. Nowakowski},
     title = {Semicommuting and commuting operators for {the~Heun} family},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a1/}
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D. Batic; D. Mills; M. Nowakowski. Semicommuting and commuting operators for the~Heun family. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 6-26. http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a1/