ABSTRACT

From (6.01) and Ritt's theorem (w.3) it follows that t'(z) = o(1) as z + oo in S,. Let z, and z, be any two distinct points of S,, labeled in such a way that IzIl <1z21. Then

f(z2) - ~ ( z I ) = (1 + ~ ) ( z ~ - z I ) , (6.03) where 9 = (5(z2)-5(zl))l(z2-zl). 6.2 The first step is to prove that when the radius a,, say, of the boundary arc of S , is sufficiently large, 191 < 1 for all z, and z, in S,. Clearly

where S is the maximum value (necessarily finite) of l['(z)l in S,, and I(z,,z,) is the length of the path of integration.