On the rate of convergence theorem for the alternate Poisson integrals for Hermite and Laguerre expansions

Authors

  • Grażyna Krech Institute of Mathematics, Pedagogical University, ul. Podchorążych 2, PL-30-084 Kraków, Poland

Abstract

The aim of this paper is the study of a rate of convergence of alternate Poisson integrals for Hermite and Laguerre expansions. We state some estimates of the rate of convergence of these integrals using the classical moduli of continuity.

References

W. Magnus, F. Oberhettinger, Formelen und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin 1948.
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B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231-242.
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G. Toczek, E. Wachnicki, On the Rate of Convergence and the Voronovskaya Theorem for the Poisson Integrals for Hermite and Laguerre Expansions, J. Approx. Theory 116 (2002), 113-125.
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Published

2004-05-22

How to Cite

Krech, G. (2004). On the rate of convergence theorem for the alternate Poisson integrals for Hermite and Laguerre expansions. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 4, 103–110. Retrieved from https://studmath.uken.krakow.pl/article/view/13312

Issue

Vol. 4 (2004): Annales Academiae Paedagogicae Cracoviensis Studia Mathematica

Section

Published