An Inequality for Derivatives of Polynomials with Positive Coefficients
โ Scribed by S.P. Zhou
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 80 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let p n z be a polynomial of degree n and D ฮฑ p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for ฮด โฅ 1 and ฮฑ โฅ 1, 2ฯ 0 D ฮฑ p n e iฮธ ฮด dฮธ 1/ฮด โค n ฮฑ + 1 F ฮด 2ฯ 0 p n e iฮธ ฮด dฮธ 1/ฮด where F ฮด = 2ฯ/ 2ฯ 0 1 + e iฮธ ฮด dฮธ 1/ฮด . We also obtain analogous inequalities
be two sequences of events, and let & N (A) and & M (B) be the number of those A i and B j , respectively, that occur. We prove that Bonferroni-type inequalities for P(& N (A) u, & M (B) v), where u and v are positive integers, are valid if and only if they are valid for a two dimensional triangular