Approximation by some combinations of Poisson integrals for Hermite and Laguerre expansions

Grażyna Krech, Eugeniusz Wachnicki

Abstract


The aim of this paper is the study of a rate of convergence of some combinations of Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals. We prove also the Voronovskaya type theorem for these new operators.

Keywords


Poisson integral; Hermite and Laguerre expansions; rate of convergence; Voronovskaya theorem

Mathematics Subject Classification


41A25; 41A30; 41A36

References


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