Abstract
In this note, we spotlight a generalization of Weierstrass integral operators introduced by Eugeniusz Wachnicki. The construction involves modified Bessel functions. The operators are correlated with diffusion equation. Our main result consists in obtaining the asymptotic expansion of derivatives of any order of Wachnicki’s operators. All coefficients are explicitly calculated, and distinct expressions are provided for analytical functions
Authors
Ulrich Abel
Fachbereich MND, Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Strasse 13, 61169, Friedberg, Germany
Octavian Agratini
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Keywords
Gauss–Weierstrass operator; Bessel function; Gamma function; hypergeometric function; asymptotic expansion
Paper coordinates
U. Abel, O. Agratini, Simultaneous approximation by Gauss-Weierstrass-Wachnicki operators, Mediterr. J. Math., 19 (2022), art. no. 267, https://doi.org/10.1007/s00009-022-02194-0
About this paper
Journal
Mediterranean Journal of Mathematics
Publisher Name
Springer
Print ISSN
1660-5446
Online ISSN
1660-5454
google scholar link
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