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 |
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.