Bailey chain method

E440256

mathematical method technique in q-series tool in partition theory

The Bailey chain method is a powerful technique in the theory of basic hypergeometric series that systematically generates infinite families of q-series and partition identities, including generalizations of Rogers–Ramanujan-type identities.

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Statements (47)

Predicate	Object
instanceOf	mathematical method ⓘ technique in q-series ⓘ tool in partition theory ⓘ
appliedIn	construction of Rogers–Ramanujan-type families ⓘ derivation of partition generating functions ⓘ proof of q-series identities ⓘ
basedOn	Bailey pair NERFINISHED ⓘ
developedInField	analytic number theory ⓘ combinatorics ⓘ
enables	systematic generation of infinite sequences of identities ⓘ
field	basic hypergeometric series ⓘ partition theory ⓘ q-series ⓘ
generalizes	classical Bailey lemma applications ⓘ
hasStep	apply Bailey lemma iteratively ⓘ obtain new Bailey pairs ⓘ start from an initial Bailey pair ⓘ translate Bailey pairs into q-series identities ⓘ
hasVariant	Bailey lattice ⓘ Bailey tree ⓘ
influenced	modern theory of basic hypergeometric series ⓘ subsequent work on partition identities ⓘ
involves	combinatorial interpretations of partitions ⓘ infinite series ⓘ q-parameter ⓘ
mathematicalDomain	series transformations ⓘ special functions ⓘ
notableFor	producing Rogers–Ramanujan-type partition identities ⓘ unifying various q-series identities ⓘ
property	algebraic ⓘ iterative ⓘ systematic ⓘ
purpose	to generalize Rogers–Ramanujan identities ⓘ to generate infinite families of q-series identities ⓘ to generate partition identities ⓘ
relatedTo	Andrews–Gordon identities NERFINISHED ⓘ Bailey lemma NERFINISHED ⓘ Bailey transform NERFINISHED ⓘ Rogers–Ramanujan identities NERFINISHED ⓘ basic hypergeometric series transformations ⓘ
usedBy	George E. Andrews NERFINISHED ⓘ researchers in partition theory ⓘ researchers in q-series ⓘ
usesConcept	Rogers–Ramanujan-type identities NERFINISHED ⓘ basic hypergeometric identities ⓘ q-series identities ⓘ q-shifted factorials ⓘ

Referenced by (1)

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

Rogers–Ramanujan-type identities → hasGeneralizationMethod → Bailey chain method ⓘ