A sharp bound for a sine polynomial
Horst Alzer; Stamatis Koumandos
Colloquium Mathematicae (2003)
- Volume: 96, Issue: 1, page 83-91
- ISSN: 0010-1354
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topHorst Alzer, and Stamatis Koumandos. "A sharp bound for a sine polynomial." Colloquium Mathematicae 96.1 (2003): 83-91. <http://eudml.org/doc/285080>.
@article{HorstAlzer2003,
abstract = {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).},
author = {Horst Alzer, Stamatis Koumandos},
journal = {Colloquium Mathematicae},
keywords = {sine polynomial; sine integral; inequalities},
language = {eng},
number = {1},
pages = {83-91},
title = {A sharp bound for a sine polynomial},
url = {http://eudml.org/doc/285080},
volume = {96},
year = {2003},
}
TY - JOUR
AU - Horst Alzer
AU - Stamatis Koumandos
TI - A sharp bound for a sine polynomial
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 1
SP - 83
EP - 91
AB - 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).
LA - eng
KW - sine polynomial; sine integral; inequalities
UR - http://eudml.org/doc/285080
ER -
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