摘要
借助单调性l’Hopital法则,研究了广义p-椭圆积分和广义反双曲正切函数,初等函数等组合的单调性,获得了广义p-椭圆积分的精确不等式,进而推广和改进了Anderson和Vuorinen关于完全椭圆积分的精确逼近.
In this paper,the authors mainly study some monotonicity properties of generalized p-elliptic integrals and inverse hyperbolic tangent function with elementary function,by applying monotone l’Hopital rule,and obtain some sharp inequalities.Meanwhile,some sharp approximations in terms of complete elliptic integrals are generalized by Anderson and Vuorinen.
作者
王飞
王婕
WANG Fei;WANG Jie(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;Department of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)
出处
《数学的实践与认识》
2021年第22期243-250,共8页
Mathematics in Practice and Theory
基金
浙江省教育厅科研基金(Y201635387)
浙江省高等学校访问学者项目(FX2018093)
浙江机电职业技术学院科教融合重点培育项目(S027120206)。
关键词
广义三角函数
广义p-椭圆积分
单调性
不等式
Gauss超几何函数
generalized trigonometric function
generalized p—elliptic integrals
monotonicity
inequalities
gaussian hypergeometric function
