On the Solution of Linear Differential Equations with Polynomial Coecients near the Origin and Infinity
Tohru Morita *
Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan.
Ken-ichi Sato
College of Engineering, Nihon University, Koriyama 963-8642, Japan.
*Author to whom correspondence should be addressed.
Abstract
A linear differential equation with polynomial coefficients is studied. In the preceding study given in J. Adv. Math. Comput. Sci. 2018; 28 (3) 1-15, the equation is expressed in terms of blocks of classified terms, and the full solutions near the origin are presented for the differential equations of the second order and with two blocks of classified terms. In the present study, it is shown that the solutions near infinity are easily obtained and the asymptotic behaviors are discussed with the aid of a theorem given in the preceding paper.
Keywords: Linear differential equations with polynomial coecients, blocks of classified terms, fractional calculus, change of variables