广义椭圆积分的两个不等式

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 46-53.

广义椭圆积分的两个不等式

尹枥, 黄利国

滨州学院理学院山东滨州 256600

收稿日期:2016-07-10 修回日期:2017-05-20 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:尹枥,yinli7979@163.com
基金资助:
国家自然科学基金（11401041）、山东省教育厅科研发展计划项目（J16li52）和滨州学院博士基金（2013Y02）

Two Inequalities Related to Generalized Elliptic Integrals

Yin Li, Huang Liguo

Department of Mathematics, Binzhou University, Shandong Binzhou 256600

Received:2016-07-10 Revised:2017-05-20 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11401041), the Science and the Technology Project of Shandong Province (J16li52) and the PhD Research Capital of Binzhou University (2013Y02)

摘要/Abstract

摘要： 研究了函数Δ_p（r）=（E_p-（r'）^pK_p）/r^p-（E'_p-r^p K'_p）/（r'）^p的单调性和凸性并给出了该函数的两个不等式，其中K_p和E_p分别是第一型和第二型广义椭圆积分.

关键词: 不等式, 广义椭圆积分, 超几何函数, 单调性, 凸性

Abstract: In this paper, the authors mainly study monotonicity and convexity of the function Δ_p (r) where K_p and E_p denote the generalized elliptic integrals of the first and second kinds, respectively. Hence, we give two new inequalities.

Key words: Inequalities, Generalized elliptic integrals, Hypergeometric function, Monotonicity, Convexity

中图分类号:

O178

尹枥, 黄利国. 广义椭圆积分的两个不等式[J]. 数学物理学报, 2018, 38(1): 46-53.

Yin Li, Huang Liguo. Two Inequalities Related to Generalized Elliptic Integrals[J]. Acta mathematica scientia,Series A, 2018, 38(1): 46-53.

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