The resurgence properties of the incomplete gamma function, I [PDF]
Studies in Applied Mathematics, 2015 In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396).
Gergő Nemes
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A Note on the Summation of the Incomplete Gamma Function [PDF]
Symmetry, 2021 We examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero distribution.
Robert Reynolds, Allan Stauffer
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New upper and lower bounds for the upper incomplete gamma function
Results in Applied MathematicsSome new upper and lower bounds for the upper incomplete gamma function Γ(a,x) are presented. Some of the bounds are given for all real x>0 and some are for only certain combinations of a and x.
Steven G. From, Suthakaran Ratnasingam
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Efficient approximation of the incomplete gamma function for use in cloud model applications [PDF]
Geoscientific Model Development, 2010 This paper describes an approximation to the lower incomplete gamma function γ<i><sub>l</sub>(a,x)</i> which has been obtained by nonlinear curve fitting. It comprises a fixed number of terms and yields moderate accuracy
U. Blahak
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A Versatile Distribution Based on the Incomplete Gamma Function: Characterization and Applications [PDF]
MathematicsIn this study, we introduce a novel distribution related to the gamma distribution, referred to as the generalized incomplete gamma distribution. This new family is defined through a stochastic representation involving a linear transformation of a random
Jimmy Reyes +3 more
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Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions [PDF]
, 2016 Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions.
T. A. Ishkhanyan +4 more
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On the incomplete gamma function and the neutrix convolution [PDF]
Mathematica Bohemica, 2003 Summary: The incomplete Gamma function \(\gamma (ab, x)\) and its associated functions \(\gamma (ab, x_+)\) and \(\gamma (ab, x_-)\) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions \(x^r\) and \(x_-^r\) are then found.
Brian Fisher +2 more
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Lévy Processes Linked to the Lower-Incomplete Gamma Function
Fractal and Fractional, 2021 We start by defining a subordinator by means of the lower-incomplete gamma function. This can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity.
Luisa Beghin, Costantino Ricciuti
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Asymptotic and exact series representations for the incomplete Gamma function [PDF]
, 2005 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,
Paolo Amore
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A Generalisation of an Expansion for the Riemann Zeta Function Involving Incomplete Gamma Functions [PDF]
, 2009 We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive integer.
R. B. Paris
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