Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914833795907584 |
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| author | Yin, Hong-Ping Han, Ling-Xiong Qi, Feng |
| author_facet | Yin, Hong-Ping Han, Ling-Xiong Qi, Feng |
| contents | In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property of a ratio between three derivatives of a function involving trigamma function and find necessary and sufficient conditions for a function defined by three derivatives of a function involving trigamma function to be completely monotonic. These results confirm previous guesses posed by Qi and generalize corresponding known conclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function Yin, Hong-Ping Han, Ling-Xiong Qi, Feng General Mathematics Primary 33B15, Secondary 26A48, 26D07, 33B10, 44A10, 44A35 In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property of a ratio between three derivatives of a function involving trigamma function and find necessary and sufficient conditions for a function defined by three derivatives of a function involving trigamma function to be completely monotonic. These results confirm previous guesses posed by Qi and generalize corresponding known conclusions. |
| title | Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function |
| topic | General Mathematics Primary 33B15, Secondary 26A48, 26D07, 33B10, 44A10, 44A35 |
| url | https://arxiv.org/abs/2405.19361 |