报告人：裘松良教授（浙江理工大学）

报告题目：The Recent Results for the Ramanujan R-Function With Applications

报告摘要：According to different requirements in applications, we present several kinds of series expansions for the Ramanujan $R$-function (or the Ramanujan constant) $R(a,c-a)=-2\gamma-\psi(a)-\psi(c-a)$ and its special case $R(a)=R(a,1-a)$, where $\psi$ is the psi function, thus providing very effective tools, techniques and methods for us to reveal  properties of $R(a,b)$ and $R(a)$. By these series expansions, some monotonicity and convexity properties and several new asymptotically sharp bounds are derived for $R(a,c-a)$ and $R(a)$, and many known results for them can be easily improved or reproved by much simpler methods. Applying these results, we can obtain some properties of the Gaussian hyper-geometric functions and the generalized quasi-conformal distortion functions. In addition, as by-products, several identities and inequalities satisfied by the Riemann zeta function and its related special functions are obtained, and a method for us to find the sum of the series $\sum_{k=1}^{\infty}(2k+1)(k^2+k)^{-n-1}$, for each natural number $n$, is presented.

报告时间：8月7日下午15：00-16：00

报告地点：数学院三楼学术报告厅

裘松良教授个人简况

    裘松良，浙江富阳人，博士、教授。曾任浙江理工大学校长、中国电子教育学会第四～第五届理事会副理事长；浙江省应用数学研究会理事长，中国纺织服装教育学会副会长；浙江大学理学院兼职教授。长期从事拟共形映照、解析函数、Ramanujan模方程与特殊函数等领域的研究，在著名的有悠久历史的Mori常数问题、Schottky上界问题等方面的研究中取得了实质性进展，其成果居世界领先水平；与M.Vuorinen等一起开创了拟共形映照、特殊函数与数论之间的交叉研究，在《中国科学》、《数学学报》、Proc. Amer. Math. Soc., SIAM J. Math. Anal., Studia Math., J. Math. Anal. Appl. 等国内外重要刊物上发表了130余篇论文，完成了数项国内外课题。多次应邀赴美国、芬兰、新西兰、香港等国家和地区学术访问、合作研究和工作。