On polynomials with curved majorants (Q581790)
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scientific article; zbMATH DE number 4129375
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On polynomials with curved majorants |
scientific article; zbMATH DE number 4129375 |
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On polynomials with curved majorants (English)
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1989
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The authors ask: Given a polynomial P of degree at most n satisfying \(0\leq P(x)\leq (1-x^ 2)^{1/2}\) for \(1<x<1\), how large can \(\max_{- \leq x\leq 1}| P'(x)|\) be? They prove an explicit bound which, as \(n\to \infty\), behaves like \((1.7424537...)n+O(1)\) and conjecture that this can be replaced by \(((\pi /2)+o(1))n\).
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majorant
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\(0\leq P(x)\leq (1-x^ 2)^{1/2}\)
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