q-Ramanujan渐近公式及q-Ramanujan R-函数  

q-Ramanujan Asymptotic Formula and q-Ramanujan R-function

作　　者：鲍琪 王淼坤[2,3] 褚玉明 Bao Qi;Wang Miaokun;Chu Yuming(School of Mathematical Sciences,East China Normal University,Shanghai 201100;Department of M athematics,Huzhou University,Zhejiang Huzhou 313000;School of Mathematics,Hangzhou Normal University,Hangzhou 311121)

机构地区：[1]华东师范大学数学科学学院,上海201100 [2]湖州师范学院理学院,浙江湖州313000 [3]杭州师范大学数学学院,杭州311121

出　　处：《数学物理学报（A辑）》2023年第6期1659-1666,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701176,11901061)。

摘　　要：该文将Gauss超几何函数_(2)F_(1)的Ramanujan渐近公式及其相关的Ramanujan R-函数推广到了基本超几何级数_(2)φ_(1)的情形.一方面,给出了_(2)φ_(1)的q-Ramanujan渐近公式并定义了q-Ramanujan R-函数;另一方面,着重研究了q-Ramanujan R-函数,证明了包括级数展开式,完全单调性和参数q的单调性在内的一些分析性质.作为应用,推导得到q-Ramanujan R-函数的几个渐近不等式.In this paper,the Ramanujan asymptotic formula of the Gaussian hypergeometric function_(2)F_(1) and its related Ramanujan R-function will be generalized to the case of basic hypergeometric series_(2)φ_(1).On the one hand,we shall present the q-Ramanujan asymptotic formula of_(2)φ_(1) and introduce the q-Ramanujan R-function;on the other hand,we shall mainly study the q-Ramanujan R-function,and prove some analytical properties of the q-Ramanujan R-function including series expansions,complete monotonicity property and monotonicity property with respect to the parameter q.As applications,several sharp inequalities for the q-Ramanujan R-function will be derived.

关 键 词：q-Ramanujan渐近公式 q-Ramanujan R-函数 Q-模拟 

分 类 号：O174.6[理学—数学]