数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 607-622.doi: 10.1016/S0252-9602(17)30026-7

• 论文 • 上一篇    下一篇

REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

王淼坤, 褚玉明   

  1. Department of Mathematics, Huzhou University, Huzhou 313000, China
  • 收稿日期:2015-07-07 修回日期:2016-06-17 出版日期:2017-06-25 发布日期:2017-06-25
  • 作者简介:Miaokun WANG,E-mail:wmk000@126.com;Yuming CHU,E-mail:chuyuming@zjhu.edu.cn
  • 基金资助:
    This research was supported by the Natural Science Foundation of China (61673169,11401191,11371125),the Tianyuan Special Funds of the Natural Science Foundation of China (11626101),and the Natural Science Foundation of the Department of Education of Zhejiang Province (201635325).

REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

Miaokun WANG, Yuming CHU   

  1. Department of Mathematics, Huzhou University, Huzhou 313000, China
  • Received:2015-07-07 Revised:2016-06-17 Online:2017-06-25 Published:2017-06-25
  • Supported by:
    This research was supported by the Natural Science Foundation of China (61673169,11401191,11371125),the Tianyuan Special Funds of the Natural Science Foundation of China (11626101),and the Natural Science Foundation of the Department of Education of Zhejiang Province (201635325).

摘要: In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

关键词: Gauss hypergeometric function, complete elliptic integrals, quadratic transformation, Ramanujan cubic transformation

Abstract: In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Key words: Gauss hypergeometric function, complete elliptic integrals, quadratic transformation, Ramanujan cubic transformation