The Laplace Transform of Composed Functions and Bivariate Bell Polynomials
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Bibliographic record
Abstract
The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell’s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica©, are given proving the effectiveness of the proposed method.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.000 | 0.000 |
| 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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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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