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The incomplete gamma function and special cases

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)

Abstract

The incomplete gamma functions γ(a, x) and Γ(a, x) are defined by
$$\gamma (a,x) = \int\limits_0^x {{t^{a - 1}}{e^{ - 1}}} dt,a > 0,{\text{ }}\Gamma (a,x) = \int\limits_x^\infty {{t^{a - 1}}{e^{ - 1}}} dt = \Gamma (a) - \gamma (a,x)$$
.

Keywords

Entire Function Branch Point Multivalued Function Elliptic Integral Differentiation Formula 
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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Literature

  1. Artin, E.: Einführung in die Theorie der Gammafunktion. Leipzig 1931.Google Scholar
  2. Erdélyi, A.: Higher Transcendental functions, Vol. II. New York: McGraw-Hill 1953.Google Scholar
  3. Erdélyi, A.: Tables of integral transforms, Vols. 1, 2. New York: McGraw-Hill 1954.Google Scholar
  4. Nielsen, N.: Theorie des Integrallogarithmus. Leipzig 1906.Google Scholar
  5. Oberhettinger, F.: Tabellen zur Fourier-Transformation. Berlin/Göttingen/Heidelberg: Springer 1957.zbMATHCrossRefGoogle Scholar
  6. Tricomi, F. G.: Funzioni ipergeometriche confluenti. Rome: Edizioni Cremonese 1954.zbMATHGoogle Scholar
  7. Whittaker, E. T., and G. N. Watson: A course of modern analysis. Cambridge: Cambridge Univ. Press 1952.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

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