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. 
@article{DEMR_2021_16_a5,
     author = {M. S. Sultanakhmedov and R. M. Gadzhimirzaev},
     title = {Representation of the solution of the {Cauchy} problem for a difference equation by a {Fourier} series in {Meixner} - {Sobolev} polynomials},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {74--82},
     publisher = {mathdoc},
     volume = {16},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2021_16_a5/}
}
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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/