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Use of Poisson's integral in calculating higher vertical derivatives of harmonic functions — Part 1

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Summary

The higher vertical derivatives of harmonic functions, expressed by Poisson's integral, are calculated for an infinite plane. The properties of the higher derivatives of the kernel of the integral are investigated and a method of calculation is proposed, which partly eliminates the negative effect caused by their “oscillation”.

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References

  1. Л. Н. Сретенский: Теория Ньютоновского потенциала. Огиз, изд. тех.-теор. лит., М.-Л. 1946.

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Authors and Affiliations

  1. Geophysical Institute, Czechosl. Acad. Sci., Prague

    Petr Velkoborský

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  1. Petr Velkoborský
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Velkoborský, P. Use of Poisson's integral in calculating higher vertical derivatives of harmonic functions — Part 1. Stud Geophys Geod 26, 3–11 (1982). https://doi.org/10.1007/BF01616120

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  • DOI: https://doi.org/10.1007/BF01616120

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