Identities for alternating inverse squared binomial and harmonic number sums

DOI10.1007/s00009-015-0574-7zbMath1343.05017OpenAlexW379674649MaRDI QIDQ305785

Anthony Sofo

Publication date: 31 August 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-015-0574-7

zbMATH Keywords

summation formulaspolylogarithm functionalternating harmonic numberscombinatorial series identitiespartial fraction approachsquared binomial coefficients

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Special sequences and polynomials (11B83)

Related Items (4)

Parametric binomial sums involving harmonic numbers ⋮ Euler sums and Stirling sums ⋮ Alternating cubic Euler sums with binomial squared terms ⋮ On some combinatorial identities and harmonic sums

Cites Work

• Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers
• Some summation formulas involving harmonic numbers and generalized harmonic numbers
• The derivative operator and harmonic number identities
• Identities for the harmonic numbers and binomial coefficients
• Summation formula involving harmonic numbers
• On generalized harmonic number sums
• The evaluation of character Euler double sums
• Integral forms of sums associated with harmonic numbers
• A formula of S. Ramanujan
• Harmonic number identities via the Newton-Andrews method
• Quadratic alternating harmonic number sums
• Sums of derivatives of binomial coefficients
• On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams
• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• Further summation formulae related to generalized harmonic numbers
• Summation formulae involving harmonic numbers
• Harmonic number identities via hypergeometric series and Bell polynomials
• Some series of the zeta and related functions
• Euler Sums and Contour Integral Representations
• Values of the polygamma functions at rational arguments
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Identities for alternating inverse squared binomial and harmonic number sums