Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions
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Bibliographic record
Abstract
Let the function f m, n (x) be given by In the present paper, we use two markedly different methods in order to prove that, among all f m, n (x)(m, n∈ℕ), only f 1, 2(x) is non-trivially completely monotonic on (0, ∞). More precisely, the functions f 1, 2(x) and f m, 2n−1(x) are completely monotonic on (0, ∞), but the functions f m, 2n (x) for (m, n)≠(1, 1) are not monotonic and do not keep the same sign on (0, ∞).
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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