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


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 coincide 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 <f,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. 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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