摘要
对r∈(0,1),称M(r)=[2r′^2K(r)K′(r)/π]+logr为Hübner函数,其中K和K′为第一类完全椭圆积分。给出了关于M(r)的一个极值问题的解,获得了M(r)的精确上下界,并运用这些结果改进了M(r)和Hersch-Pfluger偏差函数φK(r)的已知界。
For r∈(0,1),the function M(r)=[2r′~2 K(r)K′(r)/π]+logr is known as the Hübner function,where Kand K′are the complete elliptic integrals of the first kind.In this paper,the authors solve an extremal problem on the function M,and present new sharp lower and upper bounds of M(r),by which some known bounds of M(r)and the Hersch-Pfluger distortion functionφK(r)for K∈(0,∞)are improved.
作者
裘松良
鲍琪
马晗茜
QIU Songliang;BAO Qi;MA Hanxi(School of Sciences,Zhejiang Sci-Tech University,Hangzhou 310018,China)
出处
《浙江理工大学学报（自然科学版）》
2020年第3期362-367,共6页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
基金
the NSF of P.R.China(Grant No.11771400).
作者简介
Introduction to the first and corresponding author:QIU Songliang(1957-),male,Fuyang,Zhejiang,Professor,research interests:quasiconformal theory,special functions,Ramanuian′s modular equations,etc.E-mail:sl_qiu@zstu.edu.cn.Solution of an extremal problem on the Hübner function。
