Asymptotic expansion of the modified exponential integral involving the Mittag-Leffler function

2019/10/20 by R. B. Paris, R B Paris, Paris, R B
Engineering · Mathematics · #30E15 #30E20 #33E20 34E05 #Acoustic Wave Phenomena Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #math.CA #msc:30E15 #msc:30E20 #msc:33E20 #msc:34E05

paper · pdf · doi:10.48550/arxiv.1910.08957

12 pages, 0 figures

openalex publication_date 2019/10/20 · arxiv created 2020/02/19 · arxiv updated 2020/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [\it Fract. Calc. Appl. Anal. \bf 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.

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