Appell 函数和 Humbert 函数的积分表达

doi:10.12066/j.issn.1007-2861.2199

上海大学学报(自然科学版) ›› 2021, Vol. 27 ›› Issue (5): 907-918.doi: 10.12066/j.issn.1007-2861.2199

Appell 函数和 Humbert 函数的积分表达

王晓霞(), 袁学颖

上海大学理学院, 上海 200444

收稿日期:2019-09-23 出版日期:2021-10-31 发布日期:2020-01-09
通讯作者: 王晓霞 E-mail:xiaoxiawang@shu.edu.cn
作者简介:王晓霞(1980—), 女, 副教授, 博士, 研究方向为组合数学和特殊函数. E-mail: xiaoxiawang@shu.edu.cn
基金资助:
国家自然科学基金资助项目(11661032)

Integration of Appell function and Humbert function

WANG Xiaoxia(), YUAN Xueying

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2019-09-23 Online:2021-10-31 Published:2020-01-09
Contact: WANG Xiaoxia E-mail:xiaoxiawang@shu.edu.cn

摘要/Abstract

摘要：

Appell 函数和 Humbert 函数在双变量超几何函数中具有重要的研究意义. 受到 Brychkov 和 Saad 建立 Appell 函数的积分表达式的启发, 通过对双变量超几何函数与一般超几何函数积分, 建立了一些双变量超几何函数的积分表达式, 其中包含了很多 Appell 函数与 Humbert 函数的积分表达式.

关键词: Appell 函数, Humbert 函数, 双变量超几何函数

Abstract:

Appell function and Humbert function are important in the research for double hypergeometric functions. Inspired by the recent work of Brychkov and Saad, who gave some integral representations for the Appell functions, the double hypergeometric function and generalized hypergeometric function are integrated, and some integral representations are established related to double hypergeometric function including some results for Appell function and Humbert function.

Key words: Appell function, Humbert function, double hypergeometric function

中图分类号:

O157.1

王晓霞, 袁学颖. Appell 函数和 Humbert 函数的积分表达[J]. 上海大学学报(自然科学版), 2021, 27(5): 907-918.

WANG Xiaoxia, YUAN Xueying. Integration of Appell function and Humbert function[J]. Journal of Shanghai University（Natural Science Edition）, 2021, 27(5): 907-918.

参考文献 15

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Appell 函数和 Humbert 函数的积分表达

Integration of Appell function and Humbert function

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