Asymptotic Methods in Analysis
E239173
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Asymptotic Methods in Analysis canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2169652 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Asymptotic Methods in Analysis Context triple: [N. G. de Bruijn, hasPublication, Asymptotic Methods in Analysis]
-
A.
Laplace method
The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
-
B.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
E.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
- 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: Asymptotic Methods in Analysis Target entity description: Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
-
A.
Laplace method
The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
-
B.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
E.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author |
N. G. de Bruijn
ⓘ
N. G. de Bruijn ⓘ
surface form:
Nicolaas Govert de Bruijn
|
| field |
asymptotic analysis
ⓘ
mathematical analysis ⓘ number theory ⓘ |
| hasReputation |
classic reference on asymptotic methods
ⓘ
standard text in asymptotic analysis ⓘ |
| influenceOn |
analytic number theory
ⓘ
applied analysis ⓘ asymptotic enumeration in combinatorics ⓘ |
| language | English ⓘ |
| notableFor |
clarity of exposition
ⓘ
rigorous justification of asymptotic expansions ⓘ systematic treatment of asymptotic methods ⓘ |
| topic |
Laplace method
ⓘ
Mellin transform methods ⓘ Tauberian theorems ⓘ approximation of integrals ⓘ asymptotic behavior of functions ⓘ asymptotic behavior of integrals ⓘ asymptotic expansions ⓘ asymptotic series ⓘ saddle point method ⓘ stationary phase method ⓘ |
| use |
approximating functions in limiting regimes
ⓘ
approximating integrals in limiting regimes ⓘ |
| usedBy |
applied mathematicians
ⓘ
mathematicians ⓘ theoretical physicists ⓘ |
| usedIn |
advanced analysis courses
ⓘ
graduate-level number theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Asymptotic Methods in Analysis Description of subject: Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.