Asymptotic and exact series representations for the incomplete Gamma function

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Asymptotic and exact series representations for the incomplete Gamma function

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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A uniform asymptotic expansion for the incomplete gamma functions revisited

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Uniform Asymptotic Expansion for the Incomplete Beta Function

In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate...

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An asymptotic expansion for the incomplete beta function

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In a recent paper in this journal, Gautschi et al. [W. Gautschi, F.E. Harris, N.M. Temme, Expansions of the exponential integral in incomplete Gamma functions, Appl. Math. Lett. 16 (2003) 1095–1099] presented an interesting expansion formula for the exponential integral E1(z) in a series of the incomplete Gamma function γ (α, z). Their investigation was motivated by a search for better methods ...

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ژورنال

عنوان ژورنال: Europhysics Letters (EPL)

سال: 2005

ISSN: 0295-5075,1286-4854

DOI: 10.1209/epl/i2005-10066-6