Lambert W function (later named in his honor)
E279121
The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Lambert W function (distinct but historically related name) | 1 |
| Lambert W function (later named in his honor) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2566431 — 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: Lambert W function (later named in his honor) Context triple: [Johann Heinrich Lambert, knownFor, Lambert W function (later named in his honor)]
-
A.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
B.
Lindemann–Weierstrass theorem precursor
The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
-
C.
Halley’s method for solving equations
Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
-
D.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic 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: Lambert W function (later named in his honor) Target entity description: The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
-
A.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
B.
Lindemann–Weierstrass theorem precursor
The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
-
C.
Halley’s method for solving equations
Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
-
D.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
multivalued function
ⓘ
special function ⓘ |
| alsoKnownAs | product logarithm ⓘ |
| appearsIn |
closed-form solutions of some delay equations
ⓘ
closed-form solutions of some differential equations ⓘ solutions of equations of the form a x e^{b x} = c ⓘ |
| branchPoint |
z = -1/e
ⓘ
z = 0 ⓘ |
| classification | transcendental function ⓘ |
| codomain | complex numbers ⓘ |
| definesInverseOf | f(w) = w e^w ⓘ |
| domain | complex numbers ⓘ |
| growthOrder | logarithmic for large arguments ⓘ |
| hasBranch |
lower branch W_{-1}
ⓘ
principal branch W_0 ⓘ |
| hasBranchCut | (-∞,-1/e] on principal branch ⓘ |
| hasSeriesExpansionAtZero | W(z) = ∑_{n=1}^{∞} (-n)^{n-1} z^n / n! ⓘ |
| implementedIn |
MATLAB
ⓘ
Maple ⓘ CAS (Computer Algebra System) ⓘ
surface form:
Mathematica
SciPy ⓘ |
| isAnalyticOn | ℂ minus branch cuts ⓘ |
| isInverseOf | w ↦ w e^w ⓘ |
| isMultivaluedOn | [-1/e,0) ⓘ |
| isSingleValuedOn | (-1/e,∞) ⓘ |
| namedAfter | Johann Heinrich Lambert ⓘ |
| relatedTo |
exponential function
ⓘ
logarithm ⓘ tree function in combinatorics ⓘ |
| satisfiesDifferentialEquation | W'(z) = W(z) / (z (1+W(z))) ⓘ |
| satisfiesEquation | W(z) e^{W(z)} = z ⓘ |
| solvesEquationType | x e^x = z ⓘ |
| usedIn |
algorithm analysis
ⓘ
asymptotic analysis ⓘ chemical kinetics ⓘ combinatorics ⓘ control theory ⓘ delay differential equations ⓘ electrical engineering ⓘ number theory ⓘ population dynamics ⓘ quantum physics ⓘ statistical mechanics ⓘ transcendental equation solving ⓘ |
| valueAt |
W(-1/e) = -1
ⓘ
W(0) = 0 ⓘ W(e) ≈ 1 ⓘ |
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: Lambert W function (later named in his honor) Description of subject: The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Lambert W function (distinct but historically related name)