Building Generating Functions for the Sequences ???? ????+???? = ????(???? ???? + ???? ???? )
Keywords:
Sequence, polynomial function, differencing in generating function, ordinary generating function and exponential generating function.Abstract
Generating functions provide a bridge between continuous and discrete mathematics. We use generating functions to obtain recursive sequences and turn them into closed form function. This allows us to solve many complicated counting problems with very little effort. In this paper, we shall develop generalized techniques for constructing the generating functions of sequences of the form
????????+1= 2(????????+ ????????) ???????????? ???????????? ???? ≥ 0, ???? > 0 ???????????? ????0= 0
using method of differencing in generating function. Also, we shall apply the technique of generating functions in solving some important problems of recurrence relations.
