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On pseudo polar-derivatives of abstract polynomials

✍ Scribed by Neyamat Zaheer


Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
657 KB
Volume
139
Category
Article
ISSN
0022-247X

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Let p n z be a polynomial of degree n and D Ξ± p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for Ξ΄ β‰₯ 1 and Ξ± β‰₯ 1, 2Ο€ 0 D Ξ± p n e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ ≀ n Ξ± + 1 F Ξ΄ 2Ο€ 0 p n e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ where F Ξ΄ = 2Ο€/ 2Ο€ 0 1 + e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ . We also obtain analogous inequalities