Surveyor's Forum: A Recurrent Problem

Bender ' s t r ea tment of recurrences is more rigorous than it was my objective to use in the paper. T h e problem is tha t I did not ment ion how to deal with the possibility tha t c = 0. The technique I suggested is heuristic; it is intended to help one identify the proposed solution, which can then be proved correct by an inductive argument using the recursion for the inductive step. T h e me thod I proposed is simple. We make an initial guess of the order of the solution, say T ( n ) = O( fo (n ) ) , and substitute cofo(n) for T ( n ) on the right side of the recurrence. This may result in the introduction of lower-order terms f~(n), . . . , f,,(n). We then guess tha t