Asymptotic expansion of the modified exponential integral involving the mittag-leffler function

Richard Paris

doi:10.3390/math8030428

Asymptotic expansion of the modified exponential integral involving the mittag-leffler function

Richard Paris^*

^*Corresponding author for this work

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Abstract

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.

Original language	English
Article number	428
Number of pages	13
Journal	Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.3390/math8030428
Publication status	Published - 16 Mar 2020

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AB - 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.

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