Orthogonal Polynomials
E451537
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Orthogonal Polynomials canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4552549 — 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: Orthogonal Polynomials Context triple: [Gábor Szegő, notableWork, Orthogonal Polynomials]
-
A.
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.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
D.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
- 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: Orthogonal Polynomials Target entity description: Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
-
A.
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.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
D.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| associatedConcept |
Favard's theorem
NERFINISHED
ⓘ
moment functional ⓘ orthogonality with respect to a measure ⓘ three-term recurrence relation ⓘ |
| associatedWith | Gábor Szegő NERFINISHED ⓘ |
| author | Gábor Szegő NERFINISHED ⓘ |
| classification |
monograph in functional analysis
ⓘ
monograph in special functions ⓘ |
| considered |
classic reference in orthogonal polynomials
ⓘ
standard monograph in approximation theory ⓘ |
| contains |
Chebyshev polynomials
ⓘ
Christoffel–Darboux formula NERFINISHED ⓘ Hermite polynomials NERFINISHED ⓘ Jacobi polynomials NERFINISHED ⓘ Laguerre polynomials NERFINISHED ⓘ applications to Fourier series ⓘ applications to approximation theory ⓘ applications to quadrature formulas ⓘ asymptotic behavior of orthogonal polynomials ⓘ extremal properties of orthogonal polynomials ⓘ general theory of orthogonal polynomial systems ⓘ moment problems ⓘ recurrence relations for orthogonal polynomials ⓘ theory of classical orthogonal polynomials ⓘ zeros of orthogonal polynomials ⓘ |
| edition |
first edition
ⓘ
fourth edition ⓘ second edition ⓘ third edition ⓘ |
| field |
analysis
ⓘ
approximation theory ⓘ mathematics ⓘ |
| firstPublicationYear | 1939 ⓘ |
| fourthEditionEditor | Richard Askey NERFINISHED ⓘ |
| fourthEditionYear | 1975 ⓘ |
| hasInfluenceOn |
approximation theory
ⓘ
modern theory of orthogonal polynomials ⓘ numerical analysis ⓘ spectral theory ⓘ |
| language | English ⓘ |
| notableEdition | fourth edition ⓘ |
| publisher | American Mathematical Society NERFINISHED ⓘ |
| series | American Mathematical Society Colloquium Publications NERFINISHED ⓘ |
| topic | orthogonal polynomials ⓘ |
| usedAs |
graduate-level textbook
ⓘ
research reference ⓘ |
| volumeInSeries | 23 ⓘ |
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: Orthogonal Polynomials Description of subject: Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.