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Asymptotic Expansions for Second-Order Linear Difference Equations, II

    This research was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A7359.

    https://doi.org/10.1142/9789814656054_0027Cited by:1 (Source: Crossref)
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    Abstract:

    Infinite asymptotic expansions are derived for the solutions to the second order linear difference equation

    y(n+2) + nPa(n)y(n+1) + nqb(n)y(n) = 0,
    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.