| |
|
Horst Alzer and
Man Kam Kwong
On two trigonometric inequalities of Askey and Steinig
view
print
|
|
| Published: |
January 1, 2020. |
| Keywords: |
Trigonometric sums, inequalities, best possible constant. |
| Subject: |
26D05, 26D15, 33B10. |
|
|
Abstract
We prove that the inequality
(5/8)cos(x/4)+∑{[cos((k+1/4)x)]/[k+1]:1 ≤ k ≤ n} ≥ 0
as well as its companion, obtained by replacing "cos" by "sin", hold for all n ≥ 1 and x ∈ (0,2π). In both cases, the constant factor 5/8 is sharp. This refines a result of Askey and Steinig, who proved the inequalities with the factor 1 instead of 5/8. |
|
| Acknowledgements
N/A
|
|
| Author information
Horst Alzer:
Morsbacher Strasse 10
51545 Waldbröl, Germany
h.alzer@gmx.de
Man Kam Kwong:
Department of Mathematics
The Hong Kong Polytechnic University
Hunghom, Hong Kong
mankwong@connect.polyu.hk
|
|
