Integral representation of the Mittag-Leffler function

2020/01/27 by V. V. Saenko, Saenko, Viacheslav V.
Decision Sciences · Engineering · Mathematics · #33e12 #Calibration and Measurement Techniques #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Scientific Measurement and Uncertainty Evaluation #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2001.09606

openalex publication_date 2020/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using this integral representation, generalization of the integral representation of the Mittag-Leffler function has been obtained that expresses the value of this function in terms of the contour integral.

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