MathDB

Denote by

M(r,f)

the maximum modulus on the circle |z|\equal{}r of the transcendent entire function

f(z)

, and by

M_n(r,f)

that of the

nth

partial sum of the power series of

f(z)

. Prove that the existence of an entire function

f_0(z)

and a corresponding sequence of positive numbers r_1

Problem Statement