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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 398, Pages 64–86
(Mi znsl5196)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl5196 https://www.mathnet.ru/eng/znsl/v398/p64
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Abstract page: | 223 | Full-text PDF : | 59 | References: | 27 |
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