Geodesic
A sharp bound for a sine polynomial
Horst Alzer1 ; Stamatis Koumandos2
1 Morsbacher Str. 10 51545 Waldbröl, Germany
2 Department of Mathematics and Statistics The University of Cyprus P.O. Box 20537 1678 Nicosia, Cyprus
Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 83-91 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that $$ \left|\sum_{k=1}^{n}\frac{\sin((2k-1)x)}{k}\right| {\rm Si}(\pi)=1.8519\dots $$ for all integers $n\geq 1$ and real numbers $x$. The upper bound ${\rm Si}(\pi)$ is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951).
DOI : 10.4064/cm96-1-8
Keywords: prove sum frac sin k right dots integers geq real numbers upper bound best possible result refines inequalities due fej lenz

Horst Alzer 1 ; Stamatis Koumandos 2

1 Morsbacher Str. 10 51545 Waldbröl, Germany
2 Department of Mathematics and Statistics The University of Cyprus P.O. Box 20537 1678 Nicosia, Cyprus 
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Horst Alzer; Stamatis Koumandos. A sharp bound for a sine polynomial. Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 83-91. doi: 10.4064/cm96-1-8

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