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On Wachnicki’s Generalization of the Gauss–Weierstrass Integral

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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.


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

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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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Correspondence to Ulrich Abel .

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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.

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