Umbral calculus, Bailey chains, and pentagonal number theorems

DOI10.1006/jcta.2000.3111zbMath0985.11048OpenAlexW1973975822MaRDI QIDQ1584667

George E. Andrews

Publication date: 21 May 2002

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.2000.3111

zbMATH Keywords

umbral calculusJacobi triple product identityMacdonald identitiesBailey chainRogers-Ramanujan identitypentagonal number theorem

Mathematics Subject Classification ID

Umbral calculus (05A40) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elementary theory of partitions (11P81) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (13)

\texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities ⋮ The \(2\)-fold Bailey lemma and mock theta functions ⋮ An elliptic $BC_n$ Bailey Lemma, multiple Rogers–Ramanujan identities and Euler’s Pentagonal Number Theorems ⋮ Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas ⋮ Combinatorial formulas for certain sequences of multiple numbers ⋮ BILATERAL BAILEY LEMMA AND FALSE THETA FUNCTIONS ⋮ A \(U(n + 1)\) Bailey lattice ⋮ An interesting \(q\)-series related to the 4th symmetrized rank function ⋮ The \(C_n\) WP-Bailey chain ⋮ A Survey of Multipartitions Congruences and Identities ⋮ A partition identity connected to the second rank moment ⋮ THE TRI-PENTAGONAL NUMBER THEOREM AND RELATED IDENTITIES ⋮ A Bailey type identity with applications related to integer representations

Cites Work

• Multiple series Rogers-Ramanujan type identities
• Ten mathematics problems I will never solve
• Affine root systems and Dedekind's \(\eta\)-function
• An elementary proof of p(11m+6)≡0 (mod 11)
• The concept of Bailey chains
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