Sharper bounds and new proofs of the exponential function with cotangent
This paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving mo...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020450/fulltext.html |
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doaj-49c40a4f74fc474e85f1dd29ce5c3c372020-11-25T03:55:13ZengAIMS PressAIMS Mathematics2473-69882020-09-01567014704010.3934/math.2020450Sharper bounds and new proofs of the exponential function with cotangentXiangyang Wu0Kang Yang1Nichang Jiang2Xiao-Diao Chen3Key Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, ChinaKey Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, ChinaKey Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, ChinaKey Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, ChinaThis paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving more other bounding functions. Numerical experiments show that the new bounds are better than those of prevailing methods.https://www.aimspress.com/article/10.3934/math.2020450/fulltext.htmlboundsinequalitiescircular functionspáde interpolationcotangent function |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiangyang Wu Kang Yang Nichang Jiang Xiao-Diao Chen |
| spellingShingle |
Xiangyang Wu Kang Yang Nichang Jiang Xiao-Diao Chen Sharper bounds and new proofs of the exponential function with cotangent AIMS Mathematics bounds inequalities circular functions páde interpolation cotangent function |
| author_facet |
Xiangyang Wu Kang Yang Nichang Jiang Xiao-Diao Chen |
| author_sort |
Xiangyang Wu |
| title |
Sharper bounds and new proofs of the exponential function with cotangent |
| title_short |
Sharper bounds and new proofs of the exponential function with cotangent |
| title_full |
Sharper bounds and new proofs of the exponential function with cotangent |
| title_fullStr |
Sharper bounds and new proofs of the exponential function with cotangent |
| title_full_unstemmed |
Sharper bounds and new proofs of the exponential function with cotangent |
| title_sort |
sharper bounds and new proofs of the exponential function with cotangent |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2020-09-01 |
| description |
This paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving more other bounding functions. Numerical experiments show that the new bounds are better than those of prevailing methods. |
| topic |
bounds inequalities circular functions páde interpolation cotangent function |
| url |
https://www.aimspress.com/article/10.3934/math.2020450/fulltext.html |
| work_keys_str_mv |
AT xiangyangwu sharperboundsandnewproofsoftheexponentialfunctionwithcotangent AT kangyang sharperboundsandnewproofsoftheexponentialfunctionwithcotangent AT nichangjiang sharperboundsandnewproofsoftheexponentialfunctionwithcotangent AT xiaodiaochen sharperboundsandnewproofsoftheexponentialfunctionwithcotangent |
| _version_ |
1724469896378580992 |