🇫🇷 Titre (French) : Démonstration de la formule de Kyungu sur la transformée de Laplace inverse ⸻ 🇬🇧 Title (English) : Proof of Kyungu's Formula for the Inverse Laplace Transform
Bibliographic record
Abstract
🇫🇷 Description (French) Cet article présente deux démonstrations rigoureuses de la formule de Kyungu sur la transformée de Laplace inverse. La première utilise l’intégrale de Bromwich-Mellin et la seconde repose sur le développement en série entière de la fonction auxiliaire f(x) = F(1/x), suivi d’un passage terme à terme à la transformée inverse. Quatre exemples originaux sont détaillés, dont deux ne figurent pas dans les tables classiques. Cette formule ouvre la voie à de nouvelles approches analytiques en calcul de transformées inverses. 🇬🇧 Description (English) : This article provides two rigorous proofs of Kyungu’s formula for the inverse Laplace transform. The first uses the Bromwich-Mellin integral, while the second is based on a power series expansion of the auxiliary function f(x) = F(1/x), followed by termwise inversion. Four original examples are fully detailed, including two that are not found in classical tables. This formula offers a new analytical approach to inverse Laplace transform computation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.037 | 0.013 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".