Some remarks on the incomplete gamma function

  • Emin Özçağ
  • İnci Ege
  • Haşmet Gürçay
  • Biljana Jolevska-Tuneska
Conference paper


The incomplete Gamma function γ(α, x) is defined for α > 0 and x ≥ 0 by
$$ \gamma \left( {\alpha ,x} \right) = \int_0^x {u^{\alpha - 1} e^{ - u} du} $$
and by using the recurrence formula
$$ \gamma \left( {\alpha + 1,x} \right) = \alpha \gamma \left( {\alpha ,x} \right) - x^\alpha e^{ - x} $$
the definition of γ(α, x) can be extended to negative, non integer value of α. Recently Fisher et al. [FJK03] defined γ(−m, x) for m = 0, 1, 2, . . . . In this paper we consider the derivatives of the incomplete Gamma function γ(α, x) and the derivatives of locally summable function γ(α, x +) = H(x)γ(α, x) for negative integers, where H(x) denotes the Heaviside function.


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Copyright information

© Springer 2007

Authors and Affiliations

  • Emin Özçağ
    • 1
  • İnci Ege
    • 1
  • Haşmet Gürçay
    • 1
  • Biljana Jolevska-Tuneska
    • 2
  1. 1.Department of MathematicsHacettepe UniversityBeytepe, AnkaraTurkey
  2. 2.Faculty of Electrical EngineeringSkopjeRepublic of Macedonia

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