The inversion of the Laplace transform by means of generalized special series of Laguerre polynomials

I. I. Sharapudinov

Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 7-20.

Résumé

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.

Détail

Keywords: Laplace transforms, Laguerre polynomials, special series.

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