Some Evaluations On Series Expansions Of Ming Antu's Sin Function

This thesis is devoted to the so-called Ming Antu's problem and Ming Antu's theorem,which is about power series expansions of the sin(2p?)originally proposed by Mathematician Ming Antu in Qing dynasty.It consists of two parts.In Chapter one we give a short survey on the development of Ming Antu's problem up to date.Various methods and results in the past decades made by Larcombe as well as Xinrong Ma are summarized.In Chapter two,based on the our survey,we reconsider some existing results due to both Larcombe and Xinrong Ma,with a motivation to find possibly new results of Ming's problem,thereby leading us to a few new combinatorial identities for Catalan numbers.