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Transmutation of analytic and harmonic functions

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Book cover Differential Equations and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

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Abstract

Reciprocal transforms are constructed that link analytic functions in complex 3-space with harmonic functions whose angles are expressed as the spherical Euler variables in Euclidean 3-space. The representations are well suited to problems with multiple symmetry patterns along axes skewed relative to the standard spherical system. Special cases include the Bergman-Whittaker and Gilbert reciprocal integral transforms.

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References

  1. S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations, Ergebnisse der Mathematik and ihrer Grenzgebiete Band 23, Springer-Verlag, Inc., New York (1969).

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Author information

Authors and Affiliations

  1. United States Naval Academy, 21402, Annapolis, Maryland

    Peter A. McCoy

Authors
  1. Peter A. McCoy
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Ian W. Knowles Yoshimi Saitō

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© 1987 Springer-Verlag

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McCoy, P.A. (1987). Transmutation of analytic and harmonic functions. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080610

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  • DOI: https://doi.org/10.1007/BFb0080610

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

  • eBook Packages: Springer Book Archive

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