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The Integral Mittag-Leffler, Whittaker and Wright Functions

Author

Listed:
  • Alexander Apelblat

    (Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel)

  • Juan Luis González-Santander

    (Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Spain)

Abstract

Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.

Suggested Citation

  • Alexander Apelblat & Juan Luis González-Santander, 2021. "The Integral Mittag-Leffler, Whittaker and Wright Functions," Mathematics, MDPI, vol. 9(24), pages 1-34, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3255-:d:703325
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    References listed on IDEAS

    as
    1. Alexander Apelblat, 2020. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach," Mathematics, MDPI, vol. 8(5), pages 1-22, April.
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    Citations

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    Cited by:

    1. Juan Luis González-Santander & Fernando Sánchez Lasheras, 2022. "Finite and Infinite Hypergeometric Sums Involving the Digamma Function," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    2. Juan Luis González-Santander & Fernando Sánchez Lasheras, 2023. "Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

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    1. Juan Luis González-Santander & Fernando Sánchez Lasheras, 2022. "Finite and Infinite Hypergeometric Sums Involving the Digamma Function," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    2. Juan Luis González-Santander & Fernando Sánchez Lasheras, 2023. "Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

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