Askey scheme of hypergeometric orthogonal polynomials

E697762

hierarchical scheme mathematical classification scheme taxonomy of orthogonal polynomials

The Askey scheme of hypergeometric orthogonal polynomials is a hierarchical classification of families of (basic) hypergeometric orthogonal polynomials, organized by limit relations between them.

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Statements (54)

Predicate	Object
instanceOf	hierarchical scheme ⓘ mathematical classification scheme ⓘ taxonomy of orthogonal polynomials ⓘ
basedOn	limit relations between families of orthogonal polynomials ⓘ
characterizedBy	hypergeometric or basic hypergeometric representations ⓘ orthogonality relations ⓘ three-term recurrence relations ⓘ
developedBy	James Wilson NERFINISHED ⓘ
extendedTo	q-Askey scheme NERFINISHED ⓘ
field	basic hypergeometric functions ⓘ hypergeometric functions ⓘ orthogonal polynomials ⓘ special functions ⓘ
includesFamily	Al-Salam–Chihara polynomials NERFINISHED ⓘ Askey–Wilson polynomials NERFINISHED ⓘ Charlier polynomials NERFINISHED ⓘ Gegenbauer polynomials NERFINISHED ⓘ Hahn polynomials NERFINISHED ⓘ Hermite polynomials NERFINISHED ⓘ Jacobi polynomials NERFINISHED ⓘ Krawtchouk polynomials NERFINISHED ⓘ Laguerre polynomials NERFINISHED ⓘ Meixner polynomials NERFINISHED ⓘ Meixner–Pollaczek polynomials NERFINISHED ⓘ Racah polynomials NERFINISHED ⓘ Racah polynomials on finite sets ⓘ Wilson polynomials NERFINISHED ⓘ big q-Jacobi polynomials NERFINISHED ⓘ big q-Laguerre polynomials NERFINISHED ⓘ continuous Hahn polynomials NERFINISHED ⓘ continuous dual Hahn polynomials ⓘ continuous q-Jacobi polynomials NERFINISHED ⓘ continuous q-ultraspherical polynomials NERFINISHED ⓘ discrete q-Hermite polynomials NERFINISHED ⓘ dual Hahn polynomials NERFINISHED ⓘ dual q-Hahn polynomials ⓘ little q-Jacobi polynomials NERFINISHED ⓘ little q-Laguerre polynomials NERFINISHED ⓘ q-Bessel polynomials NERFINISHED ⓘ q-Charlier polynomials NERFINISHED ⓘ q-Hahn polynomials NERFINISHED ⓘ q-Krawtchouk polynomials NERFINISHED ⓘ q-Laguerre polynomials NERFINISHED ⓘ q-Meixner polynomials NERFINISHED ⓘ q-Racah polynomials NERFINISHED ⓘ
introducedBy	Richard Askey NERFINISHED ⓘ
organizedBy	degeneration limits of parameters ⓘ
organizes	basic hypergeometric orthogonal polynomials ⓘ hypergeometric orthogonal polynomials ⓘ
topFamily	Racah polynomials NERFINISHED ⓘ Wilson polynomials NERFINISHED ⓘ
usedIn	approximation theory ⓘ mathematical physics ⓘ spectral theory of operators ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jacobi polynomials → belongsTo → Askey scheme of hypergeometric orthogonal polynomials ⓘ