Asymptotic structure of solution of a certain third order differential equation in the neighborhood of a irregular singular point

In order to introduce the investigation of the present thesis,let us consider the linear homogeneous differential equation:Z2 d3y/dz3 + Z (bo + Bi Zm + b2z2m) d2y/dz2 + (Co + CiZm + C2Z) dy/dZ+ (diZm-1 + d2Z2m-1) Y = 0Here, m is a positive integer, the variable Z is complex and the constants bi, Ci (i=0,1,2) and di (i=1,2) are complex with b2 ≠ 0. It is also assumed that the roots of the indicial equation are such that the difference of no two of them is congruent to zero modulo m.Ball State UniversityMuncie, IN 47306