In mathematics, a Bailey pair is a pair of sequences satisfying certain relations, and a Bailey chain is a sequence of Bailey pairs. Bailey pairs were introduced by
W. N. Bailey (
1947,
1948) while studying the second proof Rogers 1917 of the
Rogers–Ramanujan identities, and Bailey chains were introduced by
Andrews (1984).
A pair of sequences (αn,βn) is called a Bailey pair if they are related by
or equivalently
Bailey's lemma
Bailey's lemma states that if (αn,βn) is a Bailey pair, then so is (α'n,β'n) where
In other words, given one Bailey pair, one can construct a second using the formulas above. This process can be iterated to produce an infinite sequence of Bailey pairs, called a Bailey chain.
Bailey, W. N. (1947), "Some identities in combinatory analysis", Proceedings of the London Mathematical Society, Second series, 49 (6): 421–425,
doi:
10.1112/plms/s2-49.6.421,
ISSN0024-6115,
MR0022816
Bailey, W. N. (1948), "Identities of the Rogers-Ramanujan Type", Proc. London Math. Soc., s2-50 (1): 1–10,
doi:
10.1112/plms/s2-50.1.1
Slater, L. J. (1952), "Further identities of the Rogers-Ramanujan type", Proceedings of the London Mathematical Society, Second series, 54 (2): 147–167,
doi:
10.1112/plms/s2-54.2.147,
ISSN0024-6115,
MR0049225
In mathematics, a Bailey pair is a pair of sequences satisfying certain relations, and a Bailey chain is a sequence of Bailey pairs. Bailey pairs were introduced by
W. N. Bailey (
1947,
1948) while studying the second proof Rogers 1917 of the
Rogers–Ramanujan identities, and Bailey chains were introduced by
Andrews (1984).
A pair of sequences (αn,βn) is called a Bailey pair if they are related by
or equivalently
Bailey's lemma
Bailey's lemma states that if (αn,βn) is a Bailey pair, then so is (α'n,β'n) where
In other words, given one Bailey pair, one can construct a second using the formulas above. This process can be iterated to produce an infinite sequence of Bailey pairs, called a Bailey chain.
Bailey, W. N. (1947), "Some identities in combinatory analysis", Proceedings of the London Mathematical Society, Second series, 49 (6): 421–425,
doi:
10.1112/plms/s2-49.6.421,
ISSN0024-6115,
MR0022816
Bailey, W. N. (1948), "Identities of the Rogers-Ramanujan Type", Proc. London Math. Soc., s2-50 (1): 1–10,
doi:
10.1112/plms/s2-50.1.1
Slater, L. J. (1952), "Further identities of the Rogers-Ramanujan type", Proceedings of the London Mathematical Society, Second series, 54 (2): 147–167,
doi:
10.1112/plms/s2-54.2.147,
ISSN0024-6115,
MR0049225