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Integral Representation of the Mittag-Leffler Function

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Abstract

In this paper, we obtain a generalization of the integral representation of the gamma function, which shows that the Hankel contour allows the rotation in the complex plane. The range of allowable values for the rotation angle of the contour is set. Using this integral representation, we obtain a generalization of the integral representation of the Mittag-Leffler function that expresses the value of this function through the contour integral.

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Funding

This work was supported by the Russian Foundation for Basic Research, grant nos. 19-44-730005 and 20-07-00655.

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Authors and Affiliations

  1. Ulyanovsk State University, 432017, Ulyanovsk, Russia

    V. V. Saenko

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  1. V. V. Saenko
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Correspondence to V. V. Saenko.

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Translated by A. Ivanov

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Saenko, V.V. Integral Representation of the Mittag-Leffler Function. Russ Math. 66, 43–58 (2022). https://doi.org/10.3103/S1066369X22040053

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