T h i s r e s u l t does not con ta in at a l l the a s s i g n e d coe f f i c i en t s a m and a m+ n. M o r e o v e r , for r - r 0 it w i l l be of this type only u n d e r the condi t ion l a m n = 1 l a m l 2. T h i s pape r is devoted to the so lu t ion of the above p r o b l e m for g iven va lues of the coef f i c ien t s ~m and a m + n , m _> 0, that m u s t sa t i s fy the inequa l i ty I%+.!-.< 1 ~ ] a m l 2, (4) s i nce o the rwi se we have f(z) ~-S. F i r s t of a l l we sha l l p e r f o r m an e l e m e n t a r y t r a n s f o r m a t i o n that s i m p l i f i e s the s u b s e q u e n t a n a l y s i s and c o m p u t a t i o n s ; let us in t roduce the no ta t ion