On a general \(q\)-identity

zbMath1300.05042MaRDI QIDQ405224

Aimin Xu

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p28

zbMATH Keywords

\(q\)-identityCauchy's integral formulaFaà di Bruno's formula\(q\)-generalized harmonic number\(q\)-Rice formula

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items

Combinatorial identities from contour integrals of rational functions, Some \(q\)-congruences for homogeneous and quasi-homogeneous multiple \(q\)-harmonic sums, Partition implications of a three-parameter \(q\)-series identity, Extensions of MacMahon's sums of divisors

Cites Work

• A \(q\)-analog of a general rational sum identity
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• Mellin transforms and asymptotics: Finite differences and Rice's integrals
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• On some \(q\)-identities related to divisor functions
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• Some combinatorial and analytical identities
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• Harmonic number identities via the Newton-Andrews method
• \(q\)-identities related to overpartitions and divisor functions
• Some applications of theq-Rice formula
• Summation formulae involving harmonic numbers
• Some identities involving rational sums
• Identities involving rational sums by inversion and partial fraction decomposition
• q-identities of Fu and Lascoux proved by theq-rice formula
• On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions
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