Asymptotic Expansions for Second-Order Linear Difference Equations,II

Infinite asymptotic expansions are derived for the solutions to the second-order linear difference equation where p and q are integers, a(n) and b(n) have power series expansions of the form for large values of n, and a₀ ≠ 0, b₀ ≠ 0. Recurrence relations are also given for the coefficients in the asymptotic solutions. Our proof is based on the method of successive approximations. This paper is a continuation of an earlier one, in which only the special case p ≤ 0 and q = 0 is considered.