Refined quadratic estimations of Shafer’s inequality
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 $$ \frac{\pi^{2} x}{4 +\sqrt{(\pi^{2} -4)^{2} + (2\pi x)^{2}}} < \arctan{x} < \frac{\pi^{2} x}{4 +\sqrt{32+ (2\pi x)^{2}}} $$...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-02-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1312-4 |