On the Solution of Linear Differential Equations with Polynomial Coecients near the Origin and Infinity

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.