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In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such areas as mathematical physics (in particular, the theory of random matrices), approximation theory, numerical analysis, and many others. For given polynomials and the classical orthogonal polynomials are characterized by being solutions of the differential equation

Attributes	Values
rdf:type	yago:WikicatOrthogonalPolynomials yago:WikicatSpecialHypergeometricFunctions yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921
rdfs:label	Classical orthogonal polynomials (en)
rdfs:comment	In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such areas as mathematical physics (in particular, the theory of random matrices), approximation theory, numerical analysis, and many others. For given polynomials and the classical orthogonal polynomials are characterized by being solutions of the differential equation (en)
dcterms:subject	Articles containing proofs Orthogonal polynomials Special hypergeometric functions
Wikipage page ID	336568 (xsd:integer)
Wikipage revision ID	1122481580 (xsd:integer)
Link from a Wikipage to another Wikipage	Rodrigues formula Schrödinger equation Appell sequence Approximation theory The Mathematical Intelligencer Articles containing proofs Continued fraction Gegenbauer polynomials Generalized Fourier series Eigenvalue Moment problem Thomas Joannes Stieltjes Andrey Markov Legendre polynomials Sturm–Liouville theory Adrien-Marie Legendre Mathematical analysis Pafnuty Chebyshev Chebyshev equation Differential operator Recurrence relation Hermite polynomials Jacobi polynomials Orthogonal polynomials Special hypergeometric functions Chebyshev polynomials Laguerre polynomials Binomial type Askey scheme Associated Legendre polynomials Polynomial Olinde Rodrigues Orthogonal polynomials Random matrices Sheffer sequence Continuous Fourier transform Umbral calculus Rodrigues' formula Secondary measure Springer-Verlag Biorthogonal polynomials
Link from a Wikipage to an external page	http://www.cambridge.org/us/catalogue/catalogue.asp%3Fisbn=9780521782012 https://books.google.com/books%3Fid=3hcW8HBh7gsC
sameAs	Classical orthogonal polynomials Classical orthogonal polynomials Classical orthogonal polynomials Classical orthogonal polynomials
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Harvtxt dbt:Main_article dbt:Reflist dbt:Short_description dbt:Use_American_English dbt:Su dbt:SpringerEOM dbt:Dlmf dbt:Abramowitz_Stegun_ref
Link from a Wikipa... related subject.	Orthogonal polynomials
b	n (en) r (en) r + 1 (en) r + 2 (en)
first	P. K. (en) René F. (en) Roderick S. C. (en) Roelof (en) Tom H. (en)
id	18 (xsd:integer)
last	Wong (en) Koekoek (en) Koornwinder (en) Swarttouw (en) Suetin (en)
p	[r] (en)
title	Orthogonal Polynomials (en) Classical orthogonal polynomials (en)
has abstract	In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such areas as mathematical physics (in particular, the theory of random matrices), approximation theory, numerical analysis, and many others. Classical orthogonal polynomials appeared in the early 19th century in the works of Adrien-Marie Legendre, who introduced the Legendre polynomials. In the late 19th century, the study of continued fractions to solve the moment problem by P. L. Chebyshev and then A.A. Markov and T.J. Stieltjes led to the general notion of orthogonal polynomials. For given polynomials and the classical orthogonal polynomials are characterized by being solutions of the differential equation with to be determined constants . There are several more general definitions of orthogonal classical polynomials; for example, use the term for all polynomials in the Askey scheme. (en)
prov:wasDerivedFrom	wikipedia-en:Classical_orthogonal_polynomials?oldid=1122481580&ns=0
page length (characters) of wiki page	35659 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Classical_orthogonal_polynomials
is Link from a Wikipage to another Wikipage of	List of real analysis topics Mehler–Heine formula Legendre polynomials Hahn polynomials Hermite polynomials

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