Several polynomials associated with the harmonic numbers

DOI10.1016/j.dam.2007.07.008zbMath1130.11011OpenAlexW1991518679MaRDI QIDQ2462397

Sang-Gu Lee, Gi-Sang Cheon, Suk-Geun Hwang

Publication date: 30 November 2007

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2007.07.008

zbMATH Keywords

harmonic polynomialsharmonic numbersRiordan arraysNörlund polynomialsgeneralized Stirling polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Bernoulli and Euler numbers and polynomials (11B68)

Related Items (12)

Multivariate Riordan groups and their representations ⋮ Poly-Cauchy numbers with a \(q\) parameter ⋮ Riordan arrays and harmonic number identities ⋮ Some identities of Cauchy numbers associated with continued fractions ⋮ Infinite series around multinomial coefficients and harmonic numbers ⋮ On Ward's differential calculus, Riordan matrices and Sheffer polynomials ⋮ Hypergeometric Cauchy numbers and polynomials ⋮ Sums of products of Cauchy numbers, including poly-Cauchy numbers ⋮ Shifted poly-Cauchy numbers ⋮ Generalized Riordan arrays ⋮ Hypergeometric degenerate Bernoulli polynomials and numbers ⋮ Riordan arrays and \(r\)-Stirling number identities

Cites Work

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• The Riordan group
• Riordan arrays and combinatorial sums
• A Stirling like sequence of rational numbers
• On Miki's identity for Bernoulli numbers
• Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• Multiple gamma and related functions
• Generalized harmonic numbers with Riordan arrays
• Explicit formulas for the Nörlund polynomials \(B_n^{(x)}\) and \(b_n^{(x )}\)
• The multiple gamma function and its application to computation of series
• Bernoulli matrix and its algebraic properties
• The Cauchy numbers
• Harmonic number identities and Hermite-Padé approximations to the logarithm function
• Nombres harmoniques généralisés

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