Sharp inequalities for tangent function with applications
Abstract In the article, we present new bounds for the function e t cot ( t ) − 1 $e^{t\cot(t)-1}$ on the interval ( 0 , π / 2 ) $(0, \pi/2)$ and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-05-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1372-5 |
| _version_ | 1811231774885281792 |
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| author | Hui-Lin Lv Zhen-Hang Yang Tian-Qi Luo Shen-Zhou Zheng |
| author_facet | Hui-Lin Lv Zhen-Hang Yang Tian-Qi Luo Shen-Zhou Zheng |
| author_sort | Hui-Lin Lv |
| collection | DOAJ |
| description | Abstract In the article, we present new bounds for the function e t cot ( t ) − 1 $e^{t\cot(t)-1}$ on the interval ( 0 , π / 2 ) $(0, \pi/2)$ and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function. |
| first_indexed | 2024-04-12T10:51:47Z |
| format | Article |
| id | doaj.art-00b9fff7776e48ca912cf0e3d0c7ddfb |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T10:51:47Z |
| publishDate | 2017-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-00b9fff7776e48ca912cf0e3d0c7ddfb2022-12-22T03:36:12ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-05-012017111710.1186/s13660-017-1372-5Sharp inequalities for tangent function with applicationsHui-Lin Lv0Zhen-Hang Yang1Tian-Qi Luo2Shen-Zhou Zheng3Department of Mathematics, Beijing Jiaotong UniversityDepartment of Science and Technology, State Grid Zhejiang Electric Power Company Research InstituteDepartment of Mathematics, Beijing Jiaotong UniversityDepartment of Mathematics, Beijing Jiaotong UniversityAbstract In the article, we present new bounds for the function e t cot ( t ) − 1 $e^{t\cot(t)-1}$ on the interval ( 0 , π / 2 ) $(0, \pi/2)$ and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.http://link.springer.com/article/10.1186/s13660-017-1372-5trigonometric functioninequalitiesSine integralCatalan constant |
| spellingShingle | Hui-Lin Lv Zhen-Hang Yang Tian-Qi Luo Shen-Zhou Zheng Sharp inequalities for tangent function with applications Journal of Inequalities and Applications trigonometric function inequalities Sine integral Catalan constant |
| title | Sharp inequalities for tangent function with applications |
| title_full | Sharp inequalities for tangent function with applications |
| title_fullStr | Sharp inequalities for tangent function with applications |
| title_full_unstemmed | Sharp inequalities for tangent function with applications |
| title_short | Sharp inequalities for tangent function with applications |
| title_sort | sharp inequalities for tangent function with applications |
| topic | trigonometric function inequalities Sine integral Catalan constant |
| url | http://link.springer.com/article/10.1186/s13660-017-1372-5 |
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