Finite singularities and hypergeometric solutions of linear recurrence equations (Q1295784)

Let \(L\) be the difference operators \(L=a_n\tau^n+ \cdots+ a_0\tau^0\) that acts on a function such that \[ L(f)x= a_n(x)f(x+n) +\cdots+ a_0 (x)f(n). \] The notion of finite singularities of the above difference equation is introduced. Considering left and right solutions, it is shown that a right solution can be obtained from a left solution by deforming the difference equation. Finally two theorems are proved to determine the hypergeometric solutions.