ABSTRACT
Not all of the coefficients fo, go, and g1 vanish, otherwise the singularity would be regular.
The term in the first derivative is removed from (1.01) by the substitution
Thus
where
When Izl> a, expansion gives
230 7 Differential Equations with Irregular Singularities
Sections 3 and 12 of Chapter 6 show that with appropriate restrictions equation (1.04) has solutions with the properties
y - (constant) x exp { f (pz + a In z)), (1.06) where
Returning to the original differential equation, we have from (1.03) and (1.06) w - (constant) x exp(h + p In z), (1.07)
where I = f p - + f o , P = fa-3fl.
