Note on a result of Erdős (Q919471)
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scientific article; zbMATH DE number 4161028
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on a result of Erdős |
scientific article; zbMATH DE number 4161028 |
Statements
Note on a result of Erdős (English)
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1989
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In connection with a result of \textit{P. Erdős} [Bull. Am. Math. Soc. 53, 1169-1176 (1947; Zbl 0032.38604)] the author shows that if \(P(x)=c_ n(x- x_ 1)(x-x_ 2)...(x-x_ n)\) has all its zeros in \([-1,1]\) and \(| P(\cos (k\pi /j))| \geq a>0(k=0,1,...,j)\) then \[ | c_ n| \geq 2^{(j-1)n/j}\cdot a. \]
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Chebyshev polynomials of the first kind
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