Geodesic
Higher-order Bessel equations integrable in elementary functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 140 (2017), pp. 3-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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The eigenfunction problem for a scalar Euler operator leads to an ordinary differential equation, which is an analog of higher-order Bessel equations. Its solutions are expressed through elementary functions in the case where the corresponding Euler operator can be factorized in a certain appropriate way. We obtain a formula describing such solutions. We consider the problem on common eigenfunctions of two Euler operators and present commuting Euler operators of orders $4$, $6$, and $10$ and a formula for their common eigenfunction and also commuting operators of orders $6$ and $9$.
Keywords: Euler operator, eigenfunction, commuting operators. 
@article{INTO_2017_140_a0,
     author = {Yu. Yu. Bagderina},
     title = {Higher-order {Bessel} equations integrable in elementary functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--17},
     year = {2017},
     volume = {140},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_140_a0/}
}
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Yu. Yu. Bagderina. Higher-order Bessel equations integrable in elementary functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 140 (2017), pp. 3-17. http://geodesic.mathdoc.fr/item/INTO_2017_140_a0/