Mellin Transform of an Exponential Fourier Transform Expressed in Terms of the Lerch Function
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The aim of this paper is to provide a table of definite integrals which includes both known and new integrals. This work is important because we provide a formal derivation for integrals in [7] not currently present in literature along with new integrals. By deriving new integrals we hope to expand the current list of integral formulae which could assist in research where applicable. The authors apply their contour integral method [9] to an integral in [8] to achieve this new integral formula in terms of the Lerch function. In this present work, the authors provide a formal derivation for an interesting Exponential Fourier transform and express it in terms of the Lerch function. The Exponential Fourier transform has many real world applications namely, in the field of Electrical engineering, in the work of electrical transients by [10] and in the field of Civil engineering, in the work of stress analysis of boundary load on soil by [11]. The definite integral we derived in this work is given by <img src=image/13424121_01.gif> (1) where the variables <img src=image/13424121_02.gif>. This formal derivation is then used to derive the correct version of a definite integral transform along with new formulae. Some of the results in this work are new.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
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 | 0.000 | 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 |
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 it