A \(q\)-analog of the hyperharmonic numbers

DOI10.1007/s13370-012-0106-6zbMath1306.11020OpenAlexW2071383106WikidataQ60692061 ScholiaQ60692061MaRDI QIDQ467956

Mark Shattuck, Toufik Mansour

Publication date: 5 November 2014

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-012-0106-6

zbMATH Keywords

\(q\)-analogharmonic numbershyperharmonic numbers\(r\)-Stirling numbers\(q\)-generalizationWolstenholme's theorem\(q\)-logarithm functions

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items (5)

Evaluation of various partial sums of Gaussian \(q\)-binomial sums ⋮ Summation formulas of \(q\)-hyperharmonic numbers ⋮ Identities involving harmonic and hyperharmonic numbers ⋮ Summation formulas of hyperharmonic numbers with their generalizations ⋮ Some applications on $q$-analog of the generalized hyperharmonic numbers of order $r,$ $ H_{n}^{r}(\alpha )$

Uses Software

• OEIS

Cites Work

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• The \(r\)-Stirling numbers
• Determinant expressions for \(q\)-harmonic congruences and degenerate Bernoulli numbers
• \(q\)-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher
• A Stirling like sequence of rational numbers
• On approximation measures of q-logarithms
• A q-Analogue of Wolstenholme's Harmonic Series Congruence
• Some properties of \(q\)-logarithm and \(q\)-exponential functions in Tsallis statistics

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