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Some remarks on the incomplete gamma function

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

Abstract

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.

Keywords

Asymptotic Expansion Heaviside Function Negative Integer Normal Sense Summable 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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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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