Asymptotic Expansions for Second‐Order Linear Difference Equations, II

Abstract

Infinite asymptotic expansions are derived for the solutions to the second‐order linear difference equation urn:x-wiley:00222526:media:sapm1992874289:sapm1992874289-math-0001 where p and q are integers, a ( n ) and b ( n ) have power series expansions of the form urn:x-wiley:00222526:media:sapm1992874289:sapm1992874289-math-0002 for large values of n , and a 0 ≠ 0, b 0 ≠ 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.