| Autor: |
Yusuke Nishizawa |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
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| Zdroj: |
Journal of Inequalities and Applications, Vol 2017, Iss 1, Pp 1-11 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
1029-242X |
| DOI: |
10.1186/s13660-017-1312-4 |
| Popis: |
Abstract We establish an inequality by quadratic estimations; the double inequality π 2 x 4 + ( π 2 − 4 ) 2 + ( 2 π x ) 2 < arctan x < π 2 x 4 + 32 + ( 2 π x ) 2 $$ \frac{\pi^{2} x}{4 +\sqrt{(\pi^{2} -4)^{2} + (2\pi x)^{2}}} < \arctan{x} < \frac{\pi^{2} x}{4 +\sqrt{32+ (2\pi x)^{2}}} $$ holds for x > 0 $x>0$ , where the constants ( π 2 − 4 ) 2 $(\pi^{2} -4)^{2}$ and 32 are the best possible. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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