Geodesic
Differential equations for the elementary 3-symmetric Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 64-86 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. V. Borzov; E. V. Damaskinsky. Differential equations for the elementary 3-symmetric Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 64-86. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a3/

[1] V. V. Borzov, E. V. Damaskinsky, “Connection between representations of Heisenberg and $su(1,1)$ algebra”, Days on Diffraction, 2009, 49–53

[2] V. V. Borzov, E. V. Damaskinskii, “$N$-simmetrichnye polinomy Chebysheva v sostavnoi modeli obobschennogo ostsillyatora”, TMF, 169:2 (2011), 229–240 | DOI | MR | Zbl

[3] V. V. Borzov, E. V. Damaskinskii, “Sostavnaya model obobschennogo ostsillyatora. I”, ZNS POMI, 374, 2010, 58–81 | MR | Zbl

[4] B. Beckermann, J. Gilewicz, E. Leopold, “Recurrence relation with periodic coefficients and Chebyshev polynomials”, Applicationes Mathematicae, 23 (1995), 319–323 | MR | Zbl

[5] V. V. Borzov, E. V. Damaskinsky, “Connection between representations of nonstandard and standard Chebyshev oscillators”, Days on Diffraction, 2010, 28–34

[6] V. V. Borzov, E. V. Damaskinsky, “Differentsialnye uravneniya dlya polinomov, opredelyaemykh rekurentnymi sootnosheniyami s periodicheskimi koeffitsientami”, Days on Diffraction, 2011 (to appear)

[7] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[8] S. Yu. Slavyanov, V. Lai, Spetsialnye funktsii: Edinaya teoriya, osnovannaya na analize osobennostei, “Nevskii dialekt”, SPb., 2002