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Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function

Division of Computing and Mathematics, Abertay University, Dundee DD1 1HG, UK
Mathematics 2020, 8(3), 428; https://doi.org/10.3390/math8030428
Received: 21 February 2020 / Revised: 6 March 2020 / Accepted: 10 March 2020 / Published: 16 March 2020
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics)
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]. We extend the definition of this function using the two-parameter Mittag-Leffler function. The expansions of the similarly extended sine and cosine integrals are also discussed. Numerical examples are presented to illustrate the accuracy of each type of expansion obtained. View Full-Text
Keywords: asymptotic expansions; exponential integral; Mittag-Leffler function; sine and cosine integrals asymptotic expansions; exponential integral; Mittag-Leffler function; sine and cosine integrals
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Paris, R. Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function. Mathematics 2020, 8, 428.

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