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Recent Advances in Mathematical Analysis pp 1–13Cite as

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On Wachnicki’s Generalization of the Gauss–Weierstrass Integral

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Abstract

The paper aims at a generalization of the Gauss–Weierstrass integral introduced by Eugeniusz Wachnicki two decades ago. It is intimately connected to a generalization of the heat equation. The main result is an asymptotic expansion for the operators when applied to a function belonging to a rather large class. An essential auxiliary result is a localization theorem which is interesting in itself.

Keywords

  • Gauss–Weierstrass operator
  • Bessel function
  • Kummer function
  • Asymptotic expansion
  • Degree of approximation

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Acknowledgements

The authors are grateful to the anonymous referee for valuable recommendations which led to several improvements of the manuscript. In particular, we thank for an additional reference.

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Authors and Affiliations

  1. Technische Hochschule Mittelhessen, Fachbereich MND, Friedberg, Germany

    Ulrich Abel

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

    Octavian Agratini

  3. Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

    Octavian Agratini

Authors
  1. Ulrich Abel
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  2. Octavian Agratini
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Corresponding author

Correspondence to Ulrich Abel .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Bari, Italy

    Anna Maria Candela

  2. Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Bari, Italy

    Mirella Cappelletti Montano

  3. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy

    Elisabetta Mangino

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Abel, U., Agratini, O. (2023). On Wachnicki’s Generalization of the Gauss–Weierstrass Integral. In: Candela, A.M., Cappelletti Montano, M., Mangino, E. (eds) Recent Advances in Mathematical Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-20021-2_1

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