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

### DOI: 10.31029/demr.8.2

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 , orthogonal with respect to a scalar product of Sobolev type of the following type 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.

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