Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument

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Abstract. Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of Γ(a, x) for any value of a or x. Applications ...

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ژورنال

عنوان ژورنال: Numerical Algorithms

سال: 2004

ISSN: 1017-1398

DOI: 10.1023/b:numa.0000040063.91709.58