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Published in:
2007 | OriginalPaper | Chapter
Some remarks on the incomplete gamma function
Authors : Emin Özçağ, İnci Ege, Haşmet Gürçay, Biljana Jolevska-Tuneska
Published in: Mathematical Methods in Engineering
Publisher: Springer Netherlands
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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.