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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 398, Pages 64–86 (Mi znsl5196)  
This article is cited in 1 scientific paper (total in 1 paper)

Differential equations for the elementary 3-symmetric Chebyshev polynomials

V. V. Borzova, E. V. Damaskinskyb

a St. Petersburg State University of Telecommunications, St. Petersburg, Russia
b Military Technical University, St. Petersburg, Russia
Full-text PDF (224 kB) Citations (1)
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Abstract: We continue the study of “composed model of generalized oscillator” and related simplest 3-symmetric Chebyshev polynomials. For this polynomials we obtain the second order differential equations which are of the fuchsian type. These equations have 13 singular points. The obtained results gives (in the considered simplest case) the answer on the more general question. What changes appears in the differential equations for polynomials of the Askey–Wilson scheme when the Jacobi matrix related with these polynomials was distributed by diagonal matrix with complex diagonal.
Key words and phrases: generalized oscillator, Jacobi matrix, orthogonal polynomials.
Received: 20.10.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 1, Pages 37–49
DOI: https://doi.org/10.1007/s10958-013-1371-0
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. V. Borzov, E. V. Damaskinsky, “Differential equations for the elementary 3-symmetric Chebyshev polynomials”, Questions of quantum field theory and statistical physics. Part 22, Zap. Nauchn. Sem. POMI, 398, POMI, St. Petersburg, 2012, 64–86; J. Math. Sci. (N. Y.), 192:1 (2013), 37–49
Citation in format AMSBIB
\Bibitem{BorDam12}
\by V.~V.~Borzov, E.~V.~Damaskinsky
\paper Differential equations for the elementary 3-symmetric Chebyshev polynomials
\inbook Questions of quantum field theory and statistical physics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 398
\pages 64--86
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5196}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2944989}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 1
\pages 37--49
\crossref{https://doi.org/10.1007/s10958-013-1371-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884975884}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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