Bibliographic record
Abstract
I first came across the subject of orthogonal polynomials when I was a student at Cairo University in 1964. It was part of a senior-level course on special functions taught by the late Professor Foad M. Ragab. The instructor used his own notes, which were very similar in spirit to the way Rainville treated the subject. I enjoyed Ragab's lectures and, when I started graduate school in 1968 at the Univerity of Alberta, I was fortunate to work with Waleed Al-Salam on special functions and q -series. Jerry Fields taught me asymptotics and was very generous with his time and ideas. In the late 1960s, courses in special functions were a rarity at North American universities and have been replaced by Bourbaki-type mathematics courses. In the early 1970s, Richard Askey emerged as the leader in the area of special functions and orthogonal polynomials, and the reader of this book will see the enormous impact he made on the subject of orthogonal polynomials. At the same time, George Andrews was promoting q -series and their applications to number theory and combinatorics. So when Andrews and Askey joined forces in the mid-1970s, their combined expertise advanced the subject in leaps and bounds. I was very fortunate to have been part of this group and to participate in these developments. My generation of special functions / orthogonal polynomials people owes Andrews and Askey a great deal for their ideas which fueled the subject for a while, for the leadership role they played, and for taking great care of young people.
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.
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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.545 | 0.405 |
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".