Results 11 to 20 of about 222,412 (307)
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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Inequalities for the incomplete gamma function [PDF]
Mathematical Inequalities & Applications, 2000 The incomplete gamma function \(\Gamma(a,x)\) is given by \(\Gamma (a,x)= \int^\infty_0e^{-t}t^{a-1}dt\) with \(a>0\), \(t>0\). The authors prove the following result: Let \(a\) be a positive parameter, and let \(q(x)\) be a function differentiable on \((0,\infty)\) such that \(\lim_{x\to\infty} x^ae ^{-x}q(x)=0\). If we put \(T(x)=1+(a-x)q(x)+xq'(x)\)
Pierpaolo Natalini, Biagio Palumbo
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Functional inequalities for the incomplete gamma function
Journal of Mathematical Analysis and Applications, 2012 Let \(f_a(x)= \Gamma(a,x)/\Gamma(a,0)\), where \(\Gamma(a,x)\) denotes the incomplete gamma function \((a,x> 0)\). The authors prove various new functional inequalities for \(f_a(x)\). For example, they study the double inequality \[ f_a(S_p(x_1,\dots, x_n))\leq f_a(x_1)\cdots f_a(x_n)\leq f_a(S_q(x_1,\dots, x_n)), \] where \(S_t\) is the power sum of ...
Horst Alzer, Arpad Baricz
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On existence–uniqueness results for proportional fractional differential equations and incomplete gamma functions [PDF]
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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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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The asymptotic expansion of a generalised incomplete gamma function
Journal of Computational and Applied Mathematics, 2003 The generalization has the form \(\Gamma_p(a,z)=\int_z^\infty t^{a-1} F_{2p}(t)\,dt\), where \(p=1,2,3,\ldots\) and \[ F_{2p}(t)=\sum_{k=0}^\infty (-1)^k {z^{k/p}\;\Gamma((2k+1)/(2p))\over k!\;\Gamma(k+1/2)}. \] Because \(F_2(t)=e^{-t}\), the function \(\Gamma_1(a,z)\) is the standard incomplete gamma function.
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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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Complexity, 2021 In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give a specific application for the incomplete Bessel matrix
Chaojun Zou +3 more
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Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions
Advances in Difference Equations, 2020 In this paper, we assess an integral containing incomplete H-functions and utilize it to build up an expansion formula for the incomplete H-functions including the Bessel function.
Sapna Meena +3 more
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Some generalised extended incomplete beta functions and applications
Journal of New Results in Science, 2022 This paper introduces generalised incomplete beta functions defined by the generalised beta function. Firstly, we provide some of the generalised beta function's basic properties, such as integral representations, summation formulas, Mellin transform ...
Ayşegül Çetinkaya +3 more
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