Landen transformations
E621096
Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Landen transformations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6833543 — 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: Landen transformations Context triple: [arithmetic–geometric mean identities, relatedConcept, Landen transformations]
-
A.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
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B.
Gale transform
The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
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C.
Transformations
"Transformations" is an influential art-critical work by British critic Roger Fry that explores the nature and evolution of modern art and aesthetic experience.
-
D.
Transformations
Transformations is a 1971 poetry collection by Anne Sexton that retells and darkly reimagines Grimm fairy tales through a confessional, feminist lens.
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E.
The Transformations Suite
The Transformations Suite is a politically charged multimedia jazz composition by Samora Pinderhughes that explores themes of racial injustice, incarceration, and social transformation in contemporary America.
- 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: Landen transformations Target entity description: Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
-
A.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
-
B.
Gale transform
The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
-
C.
Transformations
"Transformations" is an influential art-critical work by British critic Roger Fry that explores the nature and evolution of modern art and aesthetic experience.
-
D.
Transformations
Transformations is a 1971 poetry collection by Anne Sexton that retells and darkly reimagines Grimm fairy tales through a confessional, feminist lens.
-
E.
The Transformations Suite
The Transformations Suite is a politically charged multimedia jazz composition by Samora Pinderhughes that explores themes of racial injustice, incarceration, and social transformation in contemporary America.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
iterative transformation
ⓘ
mathematical concept ⓘ transformation of elliptic integrals ⓘ |
| appearsIn |
theory of elliptic functions
ⓘ
theory of modular equations ⓘ |
| appliesTo |
complete elliptic integral of the first kind
ⓘ
complete elliptic integral of the second kind ⓘ |
| category |
iterative algorithms in analysis
ⓘ
special functions identities ⓘ |
| definesRecurrenceFor |
modulus sequence
ⓘ
sequence of means ⓘ |
| effect |
relates E(k) to E(k_1) for transformed modulus k_1
ⓘ
relates K(k) to K(k_1) for transformed modulus k_1 ⓘ |
| field |
analysis
ⓘ
elliptic function theory ⓘ numerical analysis ⓘ |
| hasApplication |
computational mathematics
ⓘ
engineering problems with elliptic integrals ⓘ theoretical physics involving elliptic integrals ⓘ |
| hasFormula |
transformation mapping k to (1−√(1−k^2))/(1+√(1−k^2))
ⓘ
transformation mapping k to 2√k/(1+k) ⓘ |
| hasType |
ascending Landen transformation
ⓘ
descending Landen transformation ⓘ |
| historicalPeriod | 18th century ⓘ |
| namedAfter | John Landen ⓘ |
| property |
can be iterated to obtain rapidly convergent sequences
ⓘ
preserve value of certain elliptic integrals under change of modulus ⓘ |
| purpose |
acceleration of convergence in iterative schemes
ⓘ
efficient evaluation of elliptic integrals ⓘ simplification of elliptic integrals ⓘ |
| relatedTo |
Gauss transformation for elliptic integrals
ⓘ
Gauss–Landen transformations ⓘ
linked to:
Gauss transformation for elliptic integrals
duplication formulas for elliptic integrals ⓘ modular transformations ⓘ |
| relatesTo |
AGM iteration
ⓘ
arithmetic–geometric mean ⓘ
linked to:
arithmetic–geometric mean identities
complete elliptic integrals ⓘ elliptic integrals ⓘ elliptic modulus ⓘ |
| usedFor |
derivation of AGM-based algorithms
ⓘ
evaluation of elliptic integrals with different moduli from a known value ⓘ high-precision computation of π via elliptic integrals ⓘ |
| usesParameter |
complementary modulus k'
ⓘ
elliptic modulus k ⓘ |
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: Landen transformations Description of subject: Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.