ABSTRACT
The singularity of (4.01) at z = oo is classified according to the nature of the singularity of (6.01) at t = 0.
Thus infinity is an ordinary point of (4.0 1) if p (t) and q(t) are analytic a t t = 0, that is, if 22-z2f(z) and z4g(z) are analytic a t infinity. In this case all analytic solutions can be expanded in series of the form
analytic at t = 0, that is, iff@) and g (z) can be expanded in convergent series of the form
The number a is again termed the exponent of the solution or singularity. It satisfies the equation
compare (4.03) and (4.04).
