Preliminary Study On Gosper Equation

This thesis is devoted to the so-called Gosper equation a(n)x(n+1)+b(n)x(n)=c(n).It arises from the Gosper algorithm on which the famous Wilf-Zeilberger is based. It is mainly composed of the following four parts.Section 1 is a short introduction on the problem of finding series summation in closed form and Gosper equation.In Section 2 we give a full survey of the Gosper algorithm. Furthermore, a Gosper summation and its revised version are also given.As main innovative work, according to the above fact, in Section 3 we try to repre-sent the Gosper equation in terms of linear equations. And then we set up two general theorems, namely Theorems 3.4 and 3.5, for the solutions of the Gopser equation. That we obtained displays the essence of the Gosper equation more clearly than the Gosper algorithm itself.Subsequently, Section 4 investigates basic application of main theorems according as four special cases, leading to a series of Gosper summation as followsIt contains many known results due to Gosper etc. as special cases, on of which [See Eq. (45)] is...