Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 140, Pages 3–17 (Mi into230)  
This article is cited in 3 scientific papers (total in 3 papers)

Higher-order Bessel equations integrable in elementary functions

Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
Full-text PDF (196 kB) Citations (3)
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 $9$.
Keywords: Euler operator, eigenfunction, commuting operators.
Funding agency Grant number
Russian Science Foundation 14-11-00078
This work was supported by the Russian Scientific Foundation (project No. 14-11-00078).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 4, Pages 379–395
DOI: https://doi.org/10.1007/s10958-019-04431-6
Bibliographic databases:
Document Type: Article
UDC: 517.927, 517.923
MSC: 47E05, 34L10, 34B30
Language: Russian
Citation: Yu. Yu. Bagderina, “Higher-order Bessel equations integrable in elementary functions”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 140, VINITI, M., 2017, 3–17; Journal of Mathematical Sciences, 241:4 (2019), 379–395
Citation in format AMSBIB
\Bibitem{Bag17}
\by Yu.~Yu.~Bagderina
\paper Higher-order Bessel equations integrable in elementary functions
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 140
\pages 3--17
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into230}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799891}
\zmath{https://zbmath.org/?q=an:07123796}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 4
\pages 379--395
\crossref{https://doi.org/10.1007/s10958-019-04431-6}
Linking options:
  • https://www.mathnet.ru/eng/into230
  • https://www.mathnet.ru/eng/into/v140/p3
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024