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TMF, 2016, Volume 189, Number 3, Pages 371–379 (Mi tmf9229)  

This article is cited in 4 scientific papers (total in 4 papers)

Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients

S. Yu. Slavyanova, D. F. Shat'koa, A. M. Ishkhanyanbc, T. A. Rotinyana

a Saint Petersburg State University, Saint Petersburg, Russia
b Institute of Physics and Technology, Tomsk Polytechnical University, Tomsk. Russia
c Institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak-2, Armenia

Abstract: We discuss several examples of generating apparent singular points as a result of differentiating particular homogeneous linear ordinary differential equations with polynomial coefficients and formulate two general conjectures on the generation and removal of apparent singularities in arbitrary Fuchsian differential equations with polynomial coefficients. We consider a model problem in polymer physics.

Keywords: Heun-class equation, Painlevé equation, apparent singular point

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 15T-1C323
Ministry of Education and Science of the Russian Federation FTI_24_2016
The research of A. M. Ishkhanyan was supported by the Armenian State Committee of Science (SCS Grant No. 15T-1C323) and the project “Leading Russian Research Universities” (Grant No. FTI_24_2016 of Tomsk Polytechnic University).


DOI: https://doi.org/10.4213/tmf9229

Full text: PDF file (346 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 189:3, 1726–1733

Bibliographic databases:

Document Type: Article
Received: 13.05.2016

Citation: S. Yu. Slavyanov, D. F. Shat'ko, A. M. Ishkhanyan, T. A. Rotinyan, “Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients”, TMF, 189:3 (2016), 371–379; Theoret. and Math. Phys., 189:3 (2016), 1726–1733

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Slavyanov, “Symmetries and apparent singularities for the simplest Fuchsian equations”, Theoret. and Math. Phys., 193:3 (2017), 1754–1760  mathnet  crossref  crossref  adsnasa  isi  elib
    2. S. Yu. Slavyanov, A. A. Salatich, “Confluent Heun equation and confluent hypergeometric equation”, J. Math. Sci. (N. Y.), 232:2 (2018), 157–163  mathnet  crossref
    3. M. Babich, S. Slavyanov, “Antiquantization, isomonodromy, and integrability”, J. Math. Phys., 59:9, SI (2018), 091416  crossref  mathscinet  zmath  isi  scopus
    4. Ishkhanyan A.M., “Series Solutions of Confluent Heun Equations in Terms of Incomplete Gamma-Functions”, J. Appl. Anal. Comput., 9:1 (2019), 118–139  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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