Complex Analysis
E588685
Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Complex Analysis canonical | 6 |
| Complex Analysis by Elias M. Stein and Rami Shakarchi | 1 |
| Complex Analysis by Lars Ahlfors | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6376225 — 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: Complex Analysis Context triple: [Lars Ahlfors, notableWork, Complex Analysis]
-
A.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
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C.
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.
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D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
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E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- 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: Complex Analysis Target entity description: Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
-
A.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
B.
Runge approximation theorem
The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
-
C.
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.
-
D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics textbook
ⓘ
textbook on complex variables ⓘ |
| approach | rigorous ⓘ |
| audience |
mathematics students
ⓘ
theoretical physics students ⓘ |
| author |
Lars V. Ahlfors
ⓘ
linked to:
Lars Ahlfors
|
| contains |
examples
ⓘ
exercises ⓘ |
| emphasis |
rigorous proofs
ⓘ
theoretical foundations ⓘ |
| field | complex analysis ⓘ |
| focus | functions of a complex variable ⓘ |
| influenced | subsequent complex analysis textbooks ⓘ |
| language | English ⓘ |
| level |
advanced undergraduate
ⓘ
beginning graduate ⓘ |
| publisher | McGraw-Hill ⓘ |
| subject | theory of functions of a complex variable ⓘ |
| topic |
Cauchy integral formula
ⓘ
Cauchy integral theorem ⓘ Laurent series ⓘ Riemann mapping theorem ⓘ Riemann surfaces ⓘ analytic functions ⓘ argument principle ⓘ conformal mappings ⓘ entire functions ⓘ harmonic functions ⓘ maximum modulus principle ⓘ normal families ⓘ power series ⓘ residue theorem ⓘ |
| type | classic text in complex analysis ⓘ |
| usedAs | standard reference in complex analysis courses ⓘ |
| usedIn | mathematics curricula worldwide ⓘ |
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: Complex Analysis Description of subject: Complex Analysis is a classic, widely used textbook that provides a rigorous introduction to the theory of functions of a complex variable.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Complex Analysis
Cauchy integral theorem
→
standardReference
→
Complex Analysis by Elias M. Stein and Rami Shakarchi
ⓘ
linked to: Complex Analysis