Email this article Higher-Order Bessel Equations Integrable in Elementary Functions
- Authors: Bagderina Y.Y.1
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Affiliations:
- Institute of Mathematics with Computer Center of Ufa Scientific Center of Russian Academy of Sciences
- Issue: Vol 241, No 4 (2019)
- Pages: 379-395
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242900
- DOI: https://doi.org/10.1007/s10958-019-04431-6
- ID: 242900
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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.
About the authors
Yu. Yu. Bagderina
Institute of Mathematics with Computer Center of Ufa Scientific Center of Russian Academy of Sciences
Author for correspondence.
Email: bagderinayu@yandex.ru
Russian Federation, Ufa
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