Geodesic
The inversion of the Laplace transform by means of generalized special series of Laguerre polynomials
Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 7-20

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We consider the problem of inversion of the Laplace transform by means of a special series with respect to Laguerre polynomials, which in a particular case coincides with the Fourier series in polynomials $l_{r,k}^{\gamma}(x)$ $(r\in \mathbb{N}, k=0,1,\ldots)$, orthogonal with respect to a scalar product of Sobolev type of the following type \begin{equation*} ,g>=\sum\nolimits_{\nu=0}^{r-1}f^{(\nu)}(0)g^{(\nu)}(0)+\int_0^\infty f^{(r)}(t)g^{(r)}(t)t^\gamma e^{-t}dt, \gamma>-1. \end{equation*} Estimates of the approximation of functions by partial sums of a special series with respect to Laguerre polynomials are given.
Keywords: Laplace transforms, Laguerre polynomials, special series. 
@article{DEMR_2017_8_a1,
     author = {I. I. Sharapudinov},
     title = {The inversion of the {Laplace} transform by means of generalized special series of {Laguerre} polynomials},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {7--20},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_8_a1/}
}
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I. I. Sharapudinov. The inversion of the Laplace transform by means of generalized special series of Laguerre polynomials. Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 7-20. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a1/