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Higher-Order Bessel Equations Integrable in Elementary Functions

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics with Computer Center of Ufa Scientific Center of Russian Academy of Sciences, Ufa, Russia

    Yu. Yu. Bagderina

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  1. Yu. Yu. Bagderina
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Correspondence to Yu. Yu. Bagderina.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 140, Differential Equations. Mathematical Physics, 2017.

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Bagderina, Y.Y. Higher-Order Bessel Equations Integrable in Elementary Functions. J Math Sci 241, 379–395 (2019). https://doi.org/10.1007/s10958-019-04431-6

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  • DOI: https://doi.org/10.1007/s10958-019-04431-6

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