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The resurgence properties of the incomplete gamma function I [PDF]
Studies in Applied Mathematics, 2014 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).
Nemes, Gergő
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Lévy Processes Linked to the Lower-Incomplete Gamma Function [PDF]
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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Monotonicity and inequalities involving the incomplete gamma function
Journal of Inequalities and Applications, 2016 In the article, we deal with the monotonicity of the function x → [ ( x p + a ) 1 / p − x ] / I p ( x ) $x\rightarrow[ (x^{p}+a )^{1/p}-x]/I_{p}(x)$ on the interval ( 0 , ∞ ) $(0, \infty)$ for p > 1 $p>1$ and a > 0 $a>0$ , and present the necessary and ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function
Mathematics, 2021 We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function.
Robert Reynolds, Allan Stauffer
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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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Derangements and the $p$-adic incomplete gamma function. [PDF]
Transactions of the American Mathematical Society, 2020 We introduce a new $p$-adic analogue of the incomplete gamma function. We also introduce a closely related family of combinatorial sequences counting derangements and arrangements in certain wreath products.
Andrew O'Desky, David Harry Richman
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Monotonicity of the incomplete gamma function with applications
Journal of Inequalities and Applications, 2016 In the article, we discuss the monotonicity properties of the function x → ( 1 − e − a x p ) 1 / p / ∫ 0 x e − t p d t $x\rightarrow (1-e^{-ax^{p}} )^{1/p}/\int_{0}^{x}e^{-t^{p}}\,dt$ for a , p > 0 $a, p>0$ with p ≠ 1 $p\neq1$ on ( 0 , ∞ ) $(0, \infty ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
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Abstract and Applied Analysis, 2017 We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s q-integral. As applications, we derive some inequalities involving the incomplete q-Gamma function.
Kwara Nantomah
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On Extended Convex Functions via Incomplete Gamma Functions [PDF]
Journal of Function Spaces, 2021 Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties.
Yan Zhao +3 more
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Chebyshev series: Derivation and evaluation
PLoS ONE, 2023 In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial
Robert Reynolds, Allan Stauffer
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