Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives
Some complete monotonicity results that the functions ±1/e±t-1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/851213 |
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| _version_ | 1849467910434586624 |
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| author | Chun-Fu Wei Bai-Ni Guo |
| author_facet | Chun-Fu Wei Bai-Ni Guo |
| author_sort | Chun-Fu Wei |
| collection | DOAJ |
| description | Some complete monotonicity results that the functions ±1/e±t-1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on 0, ∞ are discovered. As applications of these newly discovered results, some complete monotonicity results concerning the polylogarithm are found. Finally a conjecture on the complete monotonicity of the above-mentioned ratios is posed. |
| format | Article |
| id | doaj-art-e0b9a056680a4946ad328983c9afc01a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e0b9a056680a4946ad328983c9afc01a2025-08-20T03:25:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/851213851213Complete Monotonicity of Functions Connected with the Exponential Function and DerivativesChun-Fu Wei0Bai-Ni Guo1State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, Henan 454010, ChinaSchool of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, Henan 454010, ChinaSome complete monotonicity results that the functions ±1/e±t-1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on 0, ∞ are discovered. As applications of these newly discovered results, some complete monotonicity results concerning the polylogarithm are found. Finally a conjecture on the complete monotonicity of the above-mentioned ratios is posed.http://dx.doi.org/10.1155/2014/851213 |
| spellingShingle | Chun-Fu Wei Bai-Ni Guo Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives Abstract and Applied Analysis |
| title | Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives |
| title_full | Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives |
| title_fullStr | Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives |
| title_full_unstemmed | Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives |
| title_short | Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives |
| title_sort | complete monotonicity of functions connected with the exponential function and derivatives |
| url | http://dx.doi.org/10.1155/2014/851213 |
| work_keys_str_mv | AT chunfuwei completemonotonicityoffunctionsconnectedwiththeexponentialfunctionandderivatives AT bainiguo completemonotonicityoffunctionsconnectedwiththeexponentialfunctionandderivatives |