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Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function [PDF]
Mathematics, 2020 We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [Fract. Calc. Appl. Anal. 21 (2018) 1156−1169].
Richard Paris
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Indefinite integrals involving the exponential integral function [PDF]
Integral Transforms and Special Functions, 2021 The exponential integral function Ei(x) is given as an indefinite integral of an elementary expression. This allows a second-order linear differential equation for the function to be constructed, which is of conventional form.
J. Conway
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New Approach for Calculate Exponential Integral Function
Iraqi Journal of Science, 2023 This manuscript presents a new approach to accurately calculating exponential integral function that arises in many applications such as contamination, groundwater flow, hydrological problems and mathematical physics.
L. Tawfiq, A. H. Khamas
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IEEE Access, 2016 This paper is concerned with the exponential stability analysis for time-delay systems. First, two new weighted integral inequalities are presented based on the auxiliary function-based integral inequalities.
Cheng Gong, Guopu Zhu, Ligang Wu
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Asian Research Journal of Mathematics, 2023 Motivated by the p-analogue of the exponential integral function [1], we introduce a two-parameter generalization of the Incomplete Exponential Integral function.
Ahmed Yakubu +2 more
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On Some Bounds for the Exponential Integral Function
Journal of Nepal Mathematical Society, 2021 In 1934, Hopf established an elegant inequality bounding the exponential integral function. In 1959, Gautschi established an improvement of Hopf’s results. In 1969, Luke also established two inequalities with each improving Hopf’s results. In 1997, Alzer
K. Nantomah
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A HARMONIC MEAN INEQUALITY CONCERNING THE GENERALIZED EXPONENTIAL INTEGRAL FUNCTION
Advances in Mathematics: Scientific Journal, 2021 In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where $E_k(s)$ is the generalized exponential integral function, $\Gamma(u,s)$ is the upper incomplete gamma ...
K. Nantomah
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A HARMONIC MEAN INEQUALITY FOR THE EXPONENTIAL INTEGRAL FUNCTION
International Journal of Apllied Mathematics, 2021 By using purely analytical techniques, we establish a harmonic mean inequality for the classical exponential integral function.
K. Nantomah
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Relation of Some Known Functions in terms of Generalized Meijer G-Functions
Journal of Mathematics, 2021 The aim of this paper is to prove some identities in the form of generalized Meijer G-function. We prove the relation of some known functions such as exponential functions, sine and cosine functions, product of exponential and trigonometric functions ...
Syed Ali Haider Shah +3 more
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Fractional-Modified Bessel Function of the First Kind of Integer Order
Mathematics, 2023 The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas.
Andrés Martín, Ernesto Estrada
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