Abstract
The sine polynomials of Fejér and Lukács are defined by
respectively. We prove that for all \(n\ge 2\) and \(x\in (0,\pi )\), we have
with the best possible constants
An application of the first inequality leads to a class of absolutely monotonic functions involving the arctan function.
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Alzer, H., Kwong, M.K. On the sine polynomials of Fejér and Lukács. Arch. Math. 122, 307–317 (2024). https://doi.org/10.1007/s00013-023-01950-2
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DOI: https://doi.org/10.1007/s00013-023-01950-2