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
Early online date	16 Mar 2020
DOIs	https://doi.org/10.3390/math8030428
Publication status	Published - 16 Mar 2020

Keywords

Asymptotic expansions
Exponential integral
Mittag-Lefﬂer function
Sine and cosine integrals

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10.3390/math8030428Licence: CC BY

Paris_AsymptoticExpansionOfTheModifiedExponentialIntegral_Published_2020Final published version, 369 KBLicence: CC BY

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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.",

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

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