Divergent Series
E120391
Divergent Series is a classic mathematical treatise by G. H. Hardy that systematically develops the theory and applications of divergent infinite series.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Divergent Series canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1060239 — 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: Divergent Series Context triple: [G. H. Hardy, notableWork, Divergent Series]
-
A.
The Twilight Saga film series
The Twilight Saga film series is a collection of romantic fantasy movies based on Stephenie Meyer’s novels, chronicling the supernatural love story between human Bella Swan and vampire Edward Cullen.
-
B.
Breaking Dawn
Breaking Dawn is the fourth and final novel in Stephenie Meyer’s Twilight Saga, concluding the romantic fantasy story of Bella Swan, Edward Cullen, and Jacob Black.
-
C.
Elysium
Elysium is the blissful afterlife realm in ancient Greek belief where especially virtuous or heroic souls enjoyed eternal happiness.
-
D.
Elysium
Elysium is a 2013 science fiction film directed by Neill Blomkamp, set in a dystopian future where a wealthy elite live on a luxurious space habitat while the rest of humanity struggles on an overpopulated, ruined Earth.
-
E.
The Twilight Saga: Eclipse
The Twilight Saga: Eclipse is the third film in the Twilight series, focusing on Bella Swan’s choice between vampire Edward Cullen and werewolf Jacob Black amid escalating supernatural threats.
- 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: Divergent Series Target entity description: Divergent Series is a classic mathematical treatise by G. H. Hardy that systematically develops the theory and applications of divergent infinite series.
-
A.
The Twilight Saga film series
The Twilight Saga film series is a collection of romantic fantasy movies based on Stephenie Meyer’s novels, chronicling the supernatural love story between human Bella Swan and vampire Edward Cullen.
-
B.
Breaking Dawn
Breaking Dawn is the fourth and final novel in Stephenie Meyer’s Twilight Saga, concluding the romantic fantasy story of Bella Swan, Edward Cullen, and Jacob Black.
-
C.
Elysium
Elysium is the blissful afterlife realm in ancient Greek belief where especially virtuous or heroic souls enjoyed eternal happiness.
-
D.
Elysium
Elysium is a 2013 science fiction film directed by Neill Blomkamp, set in a dystopian future where a wealthy elite live on a luxurious space habitat while the rest of humanity struggles on an overpopulated, ruined Earth.
-
E.
The Twilight Saga: Eclipse
The Twilight Saga: Eclipse is the third film in the Twilight series, focusing on Bella Swan’s choice between vampire Edward Cullen and werewolf Jacob Black amid escalating supernatural threats.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author |
G. H. Hardy
ⓘ
G. H. Hardy ⓘ
surface form:
Godfrey Harold Hardy
|
| countryOfOrigin | United Kingdom ⓘ |
| field |
infinite series
ⓘ
mathematical analysis ⓘ summability theory ⓘ |
| firstPublicationCentury | 20th century ⓘ |
| genre | mathematics ⓘ |
| hasMathematicalSubjectClassification |
40A05
ⓘ
40Cxx ⓘ 40Gxx ⓘ |
| hasPart |
appendices on special summation methods
ⓘ
applications to Dirichlet series ⓘ applications to Fourier series ⓘ historical survey of divergent series ⓘ systematic treatment of summability methods ⓘ |
| hasReputation | classic treatise in analysis ⓘ |
| influenced |
development of asymptotic analysis
ⓘ
modern theory of summability ⓘ research on divergent series in analysis ⓘ |
| intendedAudience |
advanced students of mathematics
ⓘ
professional mathematicians ⓘ |
| isCitedIn | research papers on summability theory ⓘ |
| language | English ⓘ |
| libraryOfCongressSubject |
Series, Divergent
ⓘ
Banach limit ⓘ
surface form:
Summability (Mathematics)
|
| notableFor |
classic reference on summation of divergent series
ⓘ
systematic development of the theory of divergent series ⓘ |
| publicationPlace | Oxford ⓘ |
| publisher | Oxford University Press ⓘ |
| relatedWork |
A Course of Pure Mathematics
ⓘ
Orders of Infinity ⓘ |
| series | Oxford Clarendon Press publications ⓘ |
| topic |
Abel summation
ⓘ
Borel summation ⓘ Cesàro summation ⓘ Dirichlet series ⓘ Euler–Maclaurin summation formula ⓘ
surface form:
Euler summation
Fourier analysis ⓘ
surface form:
Fourier series
Riemann–Stieltjes integral ⓘ
surface form:
Stieltjes integrals
Tauberian theorems ⓘ analytic continuation ⓘ asymptotic expansions ⓘ asymptotic series in analysis ⓘ divergent series ⓘ summation of divergent series ⓘ |
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: Divergent Series Description of subject: Divergent Series is a classic mathematical treatise by G. H. Hardy that systematically develops the theory and applications of divergent infinite series.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.