Bailey chains
E440252
Bailey chains are iterative constructions in the theory of basic hypergeometric series that generate infinite families of Rogers–Ramanujan-type identities from an initial Bailey pair.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in basic hypergeometric series
ⓘ
mathematical construction ⓘ |
| appearsIn | theory of Rogers–Ramanujan continued fraction NERFINISHED ⓘ |
| appliedIn |
combinatorial q-series identities
ⓘ
derivation of partition identities ⓘ proofs of Rogers–Ramanujan-type identities ⓘ |
| basedOn | Bailey pairs NERFINISHED ⓘ |
| constructionType | iterative construction ⓘ |
| context | theory of basic hypergeometric series ⓘ |
| developedBy | George E. Andrews NERFINISHED ⓘ |
| field |
analytic number theory
ⓘ
basic hypergeometric series ⓘ combinatorics ⓘ partition theory ⓘ q-series ⓘ |
| generalizes | Bailey lemma NERFINISHED ⓘ |
| hasKeyStep | choice of parameters in Bailey lemma ⓘ |
| historicalRoot | Bailey pairs of W. N. Bailey NERFINISHED ⓘ |
| input | initial Bailey pair ⓘ |
| inspiredBy | work of W. N. Bailey ⓘ |
| introducedBy | George E. Andrews NERFINISHED ⓘ |
| mathematicalArea |
q-hypergeometric series
ⓘ
special functions ⓘ |
| methodology | iterative application of Bailey lemma ⓘ |
| namedAfter | W. N. Bailey NERFINISHED ⓘ |
| output |
infinite family of q-series identities
ⓘ
sequence of Bailey pairs ⓘ |
| property |
can be iterated indefinitely
ⓘ
each step produces a new Bailey pair ⓘ systematic way to generate q-series identities ⓘ |
| purpose | to generate infinite families of Rogers–Ramanujan-type identities ⓘ |
| relatedTo |
Andrews–Gordon identities
NERFINISHED
ⓘ
Bailey lattice ⓘ Bailey lemma ⓘ Bailey transform ⓘ Göllnitz–Gordon identities NERFINISHED ⓘ Rogers–Ramanujan identities NERFINISHED ⓘ Rogers–Ramanujan-type identities NERFINISHED ⓘ |
| requires | initial Bailey pair relative to a parameter ⓘ |
| toolFor | systematic generation of Rogers–Ramanujan-type series-product identities ⓘ |
| usedFor |
discovering new partition theorems
ⓘ
unifying proofs of classical q-series identities ⓘ |
| usesConcept |
basic hypergeometric series summations
ⓘ
q-Pochhammer symbol NERFINISHED ⓘ q-difference equations ⓘ |
| yearIntroducedApprox | 1970s ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.