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Zap. Nauchn. Sem. POMI, 2015, Volume 432, Pages 162–176 (Mi znsl6116)  

This article is cited in 1 scientific paper (total in 1 paper)

Representations and use of symbolic computations in the theory of Heun equations

A. Ya. Kazakovab, S. Yu. Slavyanovc

a St. Petersburg State University of Technology and Design, St. Petersburg, Russia
b St. Petersburg State University of AeroSpace Instrumentation, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia

Abstract: A first-order $2\times2$ system equivalent to the Heun equation is obtained. A deformed Heun equation in symmetric form is presented. Series solutions of this equation are presented. A four-parameter subfamily of deformed confluent Heun equation whose solutions have integral representations is found.

Key words and phrases: Heun equation, deformed Heun equation, confluent Heun equation, apparent singularity, integral representations.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:6, 910–921

UDC: 517.289+517.923+517.926
Received: 21.10.2014
Language:

Citation: A. Ya. Kazakov, S. Yu. Slavyanov, “Representations and use of symbolic computations in the theory of Heun equations”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 162–176; J. Math. Sci. (N. Y.), 209:6 (2015), 910–921

Citation in format AMSBIB
\Bibitem{KazSla15}
\by A.~Ya.~Kazakov, S.~Yu.~Slavyanov
\paper Representations and use of symbolic computations in the theory of Heun equations
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 162--176
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6116}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 910--921
\crossref{https://doi.org/10.1007/s10958-015-2537-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939444439}


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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, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Записки научных семинаров ПОМИ
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