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)


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


Entire Function Branch Point Multivalued Function Elliptic Integral Differentiation Formula 
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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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