Results & Lemmas (3)
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LEMMA 1.
LEMMA 1. Let o)(s) = a zn + a +.z + be regular in A and < 1. Then |e | 5 1 ( 2. 1 ) |<o(*)| < r n ( ( H c n | ) / ( l + | e J r ) ), 1*1 =…
LEMMA 1. Let o)(s) = a zn + a +.z + be regular in A and < 1 . Then |e | 5 1 ( 2 . 1 ) |<o(*)| < r n ( ( H c n | ) / ( l + | e J r ) ) , 1*1 = r -
LEMMA 2.
LEMMA 2. Jf p(a) = 1 t J z" t V &,s^ is regular and has k=n+l Re p ( 3 ) > 0 for z € A, then, for = r, (2.3) Re p(s) > 2+bnr-bnrn-2rn+1]/…
LEMMA 2. Jf p(a) = 1 t J z" t V &,s^ is regular and has k=n+l Re p ( 3 ) > 0 for z € A , then, for \z\ = r , (2.3) Re p(s) > {2+bnr-bnrn-2rn+1]/\2+bnr+bnrn+2rn+1} (2.10 |pU)| where 0 Sf) 5 2 . 5ot?z the estimates are sharp.
LEMMA 3.
LEMMA 3. If p(z) = 1 + b zn + £ b,z is regular and has n fc=M+l K Re p(s) > 0 for z € A, then, for = r, ( 2. 8 ) | 2 f r r n- f f2n…
LEMMA 3. If p(z) = 1 + b zn + £ b,z is regular and has n fc=M+l K Re p(s) > 0 for z € A , then, for \z\ = r , ( 2 . 8 ) | 2 f r r n- f f2n https://doi.org/10.1017/S0004972700004925 Published online by Cambridge University Press
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