Triple
T22437979
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bessel functions |
E554675
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Fourier-Bessel series |
—
|
NE NERFINISHED |
How this triple was built (3 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Fourier-Bessel series | Statement: [Bessel functions, relatedTo, Fourier-Bessel series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fourier-Bessel series Context triple: [Bessel functions, relatedTo, Fourier-Bessel series]
-
A.
Bessel functions
Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
-
B.
Fourier series
A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
-
C.
Bohr–Fourier series
The Bohr–Fourier series is a generalization of the classical Fourier series that represents almost periodic functions as infinite sums of complex exponentials with possibly incommensurable frequencies.
-
D.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
E.
Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
"Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fourier-Bessel series Target entity description: A Fourier-Bessel series is an expansion of a function in terms of Bessel functions, analogous to a Fourier series but adapted to problems with cylindrical symmetry and radial coordinates.
-
A.
Bessel functions
Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
-
B.
Fourier series
A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
-
C.
Bohr–Fourier series
The Bohr–Fourier series is a generalization of the classical Fourier series that represents almost periodic functions as infinite sums of complex exponentials with possibly incommensurable frequencies.
-
D.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
E.
Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
"Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale" is a classic mathematical treatise by Ulisse Dini on Fourier series and related analytic methods for representing real-valued functions.
- F. None of above. chosen
Provenance (2 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69e11e5010e48190ae1e9c9db9697637 |
completed | April 16, 2026, 5:37 p.m. |
| NER | Named-entity recognition | batch_69f15adf52f08190a5b592be3e68af0f |
completed | April 29, 2026, 1:11 a.m. |
Created at: April 16, 2026, 8:47 p.m.