Asymptotic Expansions for Second‐Order Linear Difference Equations, II | Zendy

Wong R. | Zendy; Li H. | Zendy

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Asymptotic Expansions for Second‐Order Linear Difference Equations, II

Author(s) -

Wong R.,

Li H.

Publication year - 1992

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm1992874289

Subject(s) - mathematics , continuation , asymptotic expansion , order (exchange) , power series , series (stratigraphy) , mathematical analysis , recurrence relation , method of matched asymptotic expansions , analytic continuation , differential equation , finance , economics , paleontology , computer science , biology , programming language

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 formfor 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.

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