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

Author

Listed:
  • Richard Paris

    (Division of Computing and Mathematics, Abertay University, Dundee DD1 1HG, UK)

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.

Suggested Citation

  • Richard Paris, 2020. "Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:428-:d:333208
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