### Approximation theory

### Daghestan Electronic Mathematical Reports: Issue 8 (2017)

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

### UDK: 517.538

### Pages: 7 - 20

### 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.