Novel Results on the Multi-Parameters Mittag-Leffler Function

PAN Yu-mei, LI Yu-fen, CAI Dong-xin, YAN Xing-jie

doi:10.13371/j.cnki.chin.q.j.m.2025.01.008

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 1: 82 - 92

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.01.008

Novel Results on the Multi-Parameters Mittag-Leffler Function

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1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China; 2. Digital Communication Department, State Grid Zhangye Power Supply Company, Zhangye 734000, China

PAN Yu-mei (1997-), female, native of Weifang, Shandong, postgraduate of China University of Mining and Technology; LI Yu-fen (1985-), female, native of Ledu, Qinghai, senior engineer of State Grid Zhangye Power Supply Company, engages in power communication; CAI Dong-xin (2002-), male, native of Huainan, Anhui, undergraduate of China University of Mining and Technology; YAN Xing-jie (1981-), male, native of Lanzhou, Gansu, associate professor of China University of Mining and Technology, engages in analysis.

CAI Dong-xin (2002-), male, native of Huainan, Anhui, undergraduate of China University of Mining and Technology;

Received date: 2024-06-20

Online published: 2025-03-30

Supported by

Supported by The National Undergraduate Innovation Training Program (Grant No. 202310290069Z).

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Abstract

In this article, the multi-parameters Mittag-Leffler function is studied in detail. As a consequence, a series of novel results such as the integral representation, series representation and Mellin transform to the above function, are obtained. Especially, we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions. Meanwhile, some interesting integral operators and derivative operators of this function, are also discussed

Key words： Multi-parameters Mittag-Leffler function; Special functions; Riemann-Liouville integral

Cite this article

PAN Yu-mei, LI Yu-fen, CAI Dong-xin, YAN Xing-jie . Novel Results on the Multi-Parameters Mittag-Leffler Function[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(1) : 82 -92 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.008

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