ON THE ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF AN N-TH ORDER LINEAR DIFFERENTIAL EQUATION WITH POWER COEFFICIENTS
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor z**m multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as / z / infinite in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions); (ii) solutions which are exponentially small; (iii) solutions with a single algebraic expansion; and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neighbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m + z < 0 developed in a previous paper.
Bibliographic Reference: WRITE TO CEA MENTIONING REPORT EUR-CEA-FC-1241 EN, 1984
Record Number: 1989123031400 / Last updated on: 1987-01-01
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