The present paper is a continuation of the work initiated in [l]-. In  I gave an expansion of the form
for the second order C.F. associated with
where U8, V8, W8 satisfy a fourth-order recurrence relation, there being a similar expansion for third order C.F.'s. I shall now give simple expressions for U8, V8, W8 (or related forms) in terms of χ2s(Z1), χ2s (Z2), ω2s(Z1), ω2s(Z2), where
and show that there is a remarkable relation between the recurrence formula for the first order C.F. and that satisfied by U3, V3, W3. The generalised form of these results will be stated and proved.