Simultaneous approximation by Gauss–Weierstrass–Wachnicki operators


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


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


Gauss–Weierstrass operator; Bessel function; Gamma function; hypergeometric function; asymptotic expansion

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U. Abel, O. Agratini, Simultaneous approximation by Gauss-Weierstrass-Wachnicki operators, Mediterr. J. Math., 19 (2022), art. no. 267,


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Mediterranean Journal of Mathematics

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