高斯超几何函数的第一类幂平均界
The first type of power mean bounds for the Gaussian hypergeometric function
- Engineering Research Center of Intelligent Computing for Complex Energy Systems of Ministry of Education North China Electric Power University（教育部复杂能源系统智能计算工程研究中心 华北电力大学）
- Zhejiang Society for Electric Power（浙江省电力学会）
- Department of Mathematics and Physics North China Electric Power University（华北电力大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过特殊幂级数符号法则与超几何级数系数递推关系，得到超几何函数与幂平均间左端点处尖锐不等式的充要条件，推广了已有结果并解决了超几何均值幂平均界的剩余问题。
AI中文摘要：
本文利用一类特殊幂级数的符号法则及涉及超几何级数的系数递推关系，找到了超几何函数与幂平均（Hm-Pm不等式）之间在所有可能情形下成立的尖锐（左端点处）不等式的充要条件，这极大推广了已有结果，并解决了超几何均值的尖锐（左端点处）幂平均界的剩余问题。
英文摘要：
In this paper, by using a signs rule for a class of special power series and a recurrence relation of coefficients involving hypergeometric series, we find the necessary and sufficient conditions for the sharp (at the left endpoint) inequalities between the hypergeometric function and power mean (Hm-Pm inequality) to hold in all possible cases, which greatly extends those known results and solve the rest of problem on the sharp (at the left endpoint) power mean bounds for the hypergeometric mean.
