A sharp bound for a sine polynomial

• Autorzy: Horst Alzer , Stamatis Koumandos
• Języki publikacji: EN

Abstrakty

EN

We prove that
$|∑_{k=1}^{n} sin((2k-1)x)/k| < Si(π) = 1.8519...$
for all integers n ≥ 1 and real numbers x. The upper bound Si(π) is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951).

Kategorie tematyczne

• 26D05: Inequalities for trigonometric functions and polynomials
• 26D15: Inequalities for sums, series and integrals
• 42A05: Trigonometric polynomials, inequalities, extremal problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 1
• Strony: 83-91

Daty

wydano

2003

Twórcy

autor

Horst Alzer

• Morsbacher Str. 10, 51545 Waldbröl, Germany

autor

Stamatis Koumandos

• Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus

Identyfikatory

DOI

10.4064/cm96-1-8