Neumann series
E1162364
UNEXPLORED
The Neumann series is an infinite series expansion used to represent the inverse of an operator or solve integral and differential equations, analogous to a geometric series in functional analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Neumann series canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T15515339 — 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: Neumann series Context triple: [Born expansion of Green’s function, representationType, Neumann series]
-
A.
Hahn series
Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.
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B.
Cesàro summation
Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
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C.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
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D.
Taylor series
A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
-
E.
Lambert series
Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
- 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: Neumann series Target entity description: The Neumann series is an infinite series expansion used to represent the inverse of an operator or solve integral and differential equations, analogous to a geometric series in functional analysis.
-
A.
Hahn series
Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.
-
B.
Cesàro summation
Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
-
C.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
-
D.
Taylor series
A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
-
E.
Lambert series
Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.