Hermite polynomials
E1327679
UNEXPLORED
Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory and quantum mechanics, particularly in the analysis of the Gaussian distribution and the quantum harmonic oscillator.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hermite polynomials canonical | 7 |
| Hermite basis polynomials | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T18480250 — 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: Hermite polynomials Context triple: [Orthogonal Polynomials, contains, Hermite polynomials]
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A.
Laguerre polynomials
Laguerre polynomials are a classical family of orthogonal polynomials that arise in solutions of differential equations and play a key role in quantum mechanics and numerical analysis.
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B.
Hermite
Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
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C.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
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D.
Legendre polynomials
Legendre polynomials are a sequence of orthogonal polynomials that arise in solving Legendre’s differential equation, playing a central role in mathematical physics, especially in problems with spherical symmetry such as potential theory and quantum mechanics.
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E.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of 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: Hermite polynomials Target entity description: Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory and quantum mechanics, particularly in the analysis of the Gaussian distribution and the quantum harmonic oscillator.
-
A.
Laguerre polynomials
Laguerre polynomials are a classical family of orthogonal polynomials that arise in solutions of differential equations and play a key role in quantum mechanics and numerical analysis.
-
B.
Hermite
Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
-
C.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
D.
Legendre polynomials
Legendre polynomials are a sequence of orthogonal polynomials that arise in solving Legendre’s differential equation, playing a central role in mathematical physics, especially in problems with spherical symmetry such as potential theory and quantum mechanics.
-
E.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
- F. None of above. chosen
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.