Geodesic
Representation of the solution of the Cauchy problem for a difference equation by a Fourier series in Meixner - Sobolev polynomials
Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 74-82.

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We obtain a representation of the solution to the Cauchy problem for the $r$-th order difference equation with constant coefficients and given initial conditions at the point $x=0$. This representation is based on the expansion of the solution in the Fourier series by polynomials that are orthogonal in the sense of Sobolev on the grid $\{0, 1, \ldots\}$ and generated by the classical Meixner polynomials. In addition, an algorithm for numerical finding of the unknown coefficients in this expansion has been developed.
Keywords: Meixner polynomials, Fourier series, Sobolev orthogonal polynomials, Cauchy problem. 
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M. S. Sultanakhmedov; R. M. Gadzhimirzaev. Representation of the solution of the Cauchy problem for a difference equation by a Fourier series in Meixner - Sobolev polynomials. Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 74-82. http://geodesic.mathdoc.fr/item/DEMR_2021_16_a5/

[1] Sharapudinov I.I., Gadzhieva Z.D., “Polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Meiksnera”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:3 (2016), 310–321 | MR | Zbl

[2] Sharapudinov I.I., Gadzhieva Z.D., Gadzhimirzaev R.M., “Raznostnye uravneniya i polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Meiksnera”, Vladikavk. matem. zhurn., 19:2 (2017), 58–72 | MR | Zbl

[3] Sharapudinov I.I., Mnogochleny, ortogonalnye na setkakh, Izd-vo Dagestanskogo gos. ped. un-ta, Makhachkala, 1997

[4] Nikiforov A.F., Suslov S.K., Uvarov V.B., Klassicheskie ortogonalnye mnogochleny diskretnoi peremennoi, Nauka, M., 1985 | MR

[5] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1974