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Mittag-Leffler Functions, Related Topics and Applications pp 55–96Cite as

The Two-Parametric Mittag-Leffler Function

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Abstract

In this chapter we present the basic properties of the two-parametric Mittag-Leffler function E α, β (z) (see (1.0.3)), which is the most straightforward generalization of the classical Mittag-Leffler function E α (z) (see (3.1.1)).

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Notes

  1. 1.

    The meaning of the weak limit \(\lim _{r\rightarrow \infty }^{\!\!\!{\ast}}\) is the same as in the definition of entire functions of completely regular growth, see (4.5.1).

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Authors and Affiliations

  1. Free University Berlin Mathematical Institute, Berlin, Germany

    Rudolf Gorenflo

  2. Belarusian State University Department of Mathematics and Mechanics, Minsk, Belarus

    Anatoly A. Kilbas

  3. University of Bologna Department of Physics, Bologna, Italy

    Francesco Mainardi

  4. Belarusian State University Department of Economics, Minsk, Belarus

    Sergei V. Rogosin

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Gorenflo, R., Kilbas, A.A., Mainardi, F., Rogosin, S.V. (2014). The Two-Parametric Mittag-Leffler Function. In: Mittag-Leffler Functions, Related Topics and Applications. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43930-2_4

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