Bailey lemma
E440253
The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical lemma
ⓘ
result in q-series theory ⓘ tool in basic hypergeometric series ⓘ |
| appliesTo |
convergent q-series
ⓘ
formal power series in q ⓘ |
| category | q-series identity machinery ⓘ |
| field | mathematics ⓘ |
| generalizes | classical hypergeometric transformations to q-setting ⓘ |
| hasConcept |
Bailey chain
ⓘ
Bailey pair NERFINISHED ⓘ Bailey transform NERFINISHED ⓘ |
| hasFormulation | relation between two sequences forming a Bailey pair ⓘ |
| hasVariant |
bilateral Bailey lemma
ⓘ
limiting form of Bailey lemma ⓘ well-poised Bailey lemma NERFINISHED ⓘ |
| implies |
Andrews–Gordon identities
NERFINISHED
ⓘ
Rogers–Ramanujan identities NERFINISHED ⓘ many Rogers–Ramanujan-type partition theorems ⓘ |
| influenced |
George E. Andrews
NERFINISHED
ⓘ
subsequent work on partition identities ⓘ |
| introducedBy | W. N. Bailey NERFINISHED ⓘ |
| involves |
basic hypergeometric series notation
ⓘ
q-Pochhammer symbol ⓘ q-shifted factorials ⓘ |
| namedAfter | W. N. Bailey NERFINISHED ⓘ |
| relatedTo |
Andrews–Gordon identities
NERFINISHED
ⓘ
Bailey lattice ⓘ Rogers–Fine identity NERFINISHED ⓘ Rogers–Ramanujan identities NERFINISHED ⓘ q-binomial theorem NERFINISHED ⓘ |
| relates | Bailey pairs relative to a parameter a ⓘ |
| subfield |
analytic number theory
ⓘ
basic hypergeometric series ⓘ combinatorics ⓘ q-series ⓘ |
| typicalConclusion | produces a new Bailey pair (α'_n, β'_n) relative to the same parameter ⓘ |
| typicalHypothesis | given a Bailey pair (α_n, β_n) relative to a ⓘ |
| usedFor |
constructing infinite families of q-identities
ⓘ
deriving q-series identities ⓘ generating Rogers–Ramanujan-type identities ⓘ producing Bailey chains ⓘ producing Bailey pairs ⓘ proving partition identities ⓘ transforming basic hypergeometric series ⓘ |
| usedIn |
combinatorial proofs of partition theorems
ⓘ
proofs of modular-type q-series identities ⓘ theory of mock theta functions ⓘ |
| yearIntroduced | 1940s ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.