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A child's garden of special functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

A great many of the special functions of mathematical physics which arise in particular problems can be expressed as a chain of homogeneous fractional-Laplace operators. A convenient way of cataloging these formulas is given by the G-function of Meijer. We define these operators and apply them to a few simple examples.

Keywords

  • Special Function
  • Series Expansion
  • Hypergeometric Function
  • Modify Bessel Function
  • Transcendental Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Meller, N. A., “On Certain Applications of the Operational Calculus to Problems of Analysis,” Zh. vych. mat., 3, No 1(1963) pp 71–78

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  5. Luke, Y., The Special Functions and Their Approximations, vol. 1 and 2, Academic Press (1969)

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© 1975 Springer-Verlag

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Higgins, T.P. (1975). A child's garden of special functions. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067106

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  • DOI: https://doi.org/10.1007/BFb0067106

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

  • eBook Packages: Springer Book Archive