Cite this article as:
Sharapudinov I. I., Guseinov I. G. Polynomials Orthogonal with Respect to Sobolev Type Inner Product Generated by Charlier Polynomials. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2018, vol. 18, iss. 2, pp. 196-205. DOI: https://doi.org/10.18500/1816-9791-2018-18-2-196-205
Polynomials Orthogonal with Respect to Sobolev Type Inner Product Generated by Charlier Polynomials
The problem of constructing of the Sobol ev orthogonal polynomials sαr,n(x) generated by Char li er polynomialssαn(x) is considered. It is shown that the system of polynomials sαr,n(x) generated by Charlier polynomialsis complete in the space Wrl, consisted of the discrete functions, given on the grid Ω = {0, 1, . . .}. Wrlρisa H ilb ert space with the inner product hf, gi. An explicit formula in the form of sαr,k+r(x) =kPl=0brlx[l+r],where xm]= x(x −1) . . . (x − m + 1), is found. The connection between the polynomials sαr,n(x) and the classical Charlier polynomials sαn(x) in the form of sαr,k+r(x) = Urk·sαk+r(x) −r−1Pν=0Vrk,νx[ν]¸, wherefor the numbers Urk, Vrk,ν we found the explicit expressions, is established.
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