Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

DOI10.1186/1029-242X-2013-49zbMath1283.11115OpenAlexW2025891270WikidataQ59294142 ScholiaQ59294142MaRDI QIDQ395810

Junesang Choi

Publication date: 30 January 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2013-49

zbMATH Keywords

Hurwitz zeta functionRiemann zeta functionharmonic numberspolygamma functionsStirling numbers of the first kindgeneralized harmonic numbersgeneralized hypergeometric function \(_pF_q\)psi-functionsummation formulas for\(_pF_q\)

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Other Dirichlet series and zeta functions (11M41) Other functions defined by series and integrals (33E20) Hurwitz and Lerch zeta functions (11M35) Function-theoretic methods (including power series methods and semicontinuous methods) for summability (40C15)

Related Items (18)

Some evaluations of parametric Euler type sums of harmonic numbers ⋮ Generalized log-sine integrals and Bell polynomials ⋮ Identities for alternating inverse squared binomial and harmonic number sums ⋮ The Roman harmonic numbers revisited ⋮ Some identities on generalized harmonic numbers and generalized harmonic functions ⋮ Derivation of computational formulas for certain class of finite sums: Approach to generating functions arising from p$$ p $$‐adic integrals and special functions ⋮ Extensions of some known algebraic and combinatorial identities ⋮ New series with Cauchy and Stirling numbers, Part 2 ⋮ Harmonic number identities via polynomials with \(r\)-Lah coefficients ⋮ Some results on \(q\)-harmonic number sums ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ Half-integer values of the sums of harmonic numbers of order two ⋮ New families of alternating harmonic number sums ⋮ Unnamed Item ⋮ Quadratic alternating harmonic number sums ⋮ Applications of derivative and difference operators on some sequences

Cites Work

• Some summation formulas involving harmonic numbers and generalized harmonic numbers
• Identities for the harmonic numbers and binomial coefficients
• Certain summation formulas involving harmonic numbers and generalized harmonic numbers
• Series involving the zeta function and multiple Gamma functions
• A note on harmonic numbers, umbral calculus and generating functions
• Computer proofs of a new family of harmonic number identities.
• Hypergeometric series and harmonic number identities
• Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• The Dattoli-Srivastava conjectures concerning generating functions involving the harmonic numbers
• Combinatorial sums and finite differences
• On some series representations of the Hurwitz zeta function
• Series representations for some mathematical constants

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