# 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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