Beyond the Beta Integral Method: Transformation Formulas for Hypergeometric Functions via Meijer's G Function

被引：4
作者：
Karp, Dmitrii [1 ,2 ]
Prilepkina, Elena [2 ,3 ]
机构：
[1] Holon Inst Technol, Dept Math, IL-5810201 Holon, Israel
[2] Far Eastern Fed Univ, Vladivostok 690091, Russia
[3] Inst Appl Math FEBRAS, Vladivostok 690041, Russia
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 08期
关键词：
generalized hypergeometric function; hypergeometric identity; Miller-Paris transformations; summation formulas; Meijer's G function; EXTENSIONS; SERIES; IDENTITIES; SUMMATION;
D O I：
10.3390/sym14081541
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The beta integral method proved itself as a simple but nonetheless powerful method for generating hypergeometric identities at a fixed argument. In this paper, we propose a generalization by substituting the beta density with a particular type of Meijer's G function. By the application of our method to known transformation formulas, we derive about forty hypergeometric identities, the majority of which are believed to be new.
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页数：31
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