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A Versatile Distribution Based on the Incomplete Gamma Function: Characterization and Applications
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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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 A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS
Malaysian Journal of Computing, 2021 Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, further generalized extended beta function with some of its properties like summation
Umar Muhammad Abubakar, Saroj Patel
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Extended incomplete gamma functions with applications
Journal of Mathematical Analysis and Applications, 2002 In this paper the authors introduce the following functions \[ \gamma (\alpha,x; b,\beta)= \int^x_0 t^{\alpha-1} e^{-t-bt^{-\beta}} dt,\;x\geq 0,\;b\geq 0, \] and \[ \Gamma (\alpha,x;b, \beta)=\int^\infty_x t^{\alpha-1} e^{-t-bt^{-\beta}}dt,\;x\geq 0,\;b\geq 0, \] and call them extended incomplete gamma functions.
Chaudhry, M.Aslam, Zubair, S.M.
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On the expansion of the Kummer function in terms of incomplete Gamma functions
, 2003 The expansion of Kummer's hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable.
Morosi, Carlo, Pizzocchero, Livio
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Counting and Computing by $e$ [PDF]
, 2005 In this paper we count the number of paths and cycles in complete graphs by using the number $e$. Also, we compute the number of derangements in same way.
Hassani, Mehdi
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Generalized incomplete gamma functions with applications
Journal of Computational and Applied Mathematics, 1994 The authors introduce the following generalization of the incomplete gamma function: \[ \int^\infty_x e^{-t} t^{\alpha - 1} e^{- t - b/t} dt, \quad \text{Re} (\alpha),\;b > 0, \] and its complement. These have been found useful in their researches in heat conduction, probability theory and in the study of Fourier and Laplace transforms.
Chaudhry, M.Aslam, Zubair, S.M.
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Advances in Difference Equations, 2020 In this article, we employ the lower regularized incomplete gamma functions to demonstrate the existence and uniqueness of solutions for fractional differential equations involving nonlocal fractional derivatives (GPF derivatives) generated by ...
Zaid Laadjal +2 more
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Fractal and FractionalIn this paper, we evaluate a general class of finite integrals involving the error function, generalized Mittag-Leffler functions, and incomplete Aleph functions. The main result provides a unified framework that extends several known formulas related to
Dinesh Kumar +4 more
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AIP Advances, 2011 By introducing a cutoff on the cumulative measure of a force, a unified kinetic theory is developed for both rigid-sphere and inverse-square force laws.
Yongbin Chang, Larry A. Viehland
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