Quadratic alternating harmonic number sums

DOI10.1016/j.jnt.2015.02.013zbMath1310.05014OpenAlexW2063111660MaRDI QIDQ2343178

Anthony Sofo

Publication date: 4 May 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.02.013

zbMATH Keywords

summation formulasbinomial coefficientspolylogarithm functionalternating harmonic numberscombinatorial series identitiespartial fraction approach

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 (52)

Euler sums and integrals of polylogarithm functions ⋮ Some evaluations of parametric Euler type sums of harmonic numbers ⋮ Integrals of inverse trigonometric and polylogarithmic functions ⋮ Parametric binomial sums involving harmonic numbers ⋮ Euler-type sums involving multiple harmonic sums and binomial coefficients ⋮ A master integral in four parameters ⋮ Identities for alternating inverse squared binomial and harmonic number sums ⋮ Unnamed Item ⋮ On harmonic numbers and nonlinear Euler sums ⋮ Extension of the four Euler sums being linear with parameters and series involving the zeta functions ⋮ Quadratic and cubic harmonic number sums ⋮ New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ Some evaluation of parametric Euler sums ⋮ Integrals of polylogarithms and infinite series involving generalized harmonic numbers ⋮ Euler sums and Stirling sums ⋮ Summation formulas involving generalized harmonic numbers ⋮ Explicit evaluation of quadratic Euler sums ⋮ Theory and computation of Euler sums of generalized hyperharmonic numbers ⋮ Euler sums of generalized hyperharmonic numbers ⋮ Some results on \(q\)-harmonic number sums ⋮ Unnamed Item ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ New results containing quadratic harmonic numbers ⋮ Half-integer values of the sums of harmonic numbers of order two ⋮ Zeta identities in parameter form ⋮ Integrals of polylogarithmic functions with negative argument ⋮ Unnamed Item ⋮ New families of alternating harmonic number sums ⋮ Tornheim type series and nonlinear Euler sums ⋮ Alternating cubic Euler sums with binomial squared terms ⋮ A Saalschütz-type identity and summation formulae involving generalized harmonic numbers ⋮ General order Euler sums with multiple argument ⋮ Explicit evaluations of sums of sequence tails ⋮ Unnamed Item ⋮ Explicit evaluation of harmonic sums ⋮ Whipple-type 3F2-series and summation formulae involving generalized harmonic numbers ⋮ General order Euler sums with rational argument ⋮ Watson-type₃F₂-series and summation formulae involving generalized harmonic numbers ⋮ Four parametric linear Euler sums ⋮ Harmonic numbers at half integer values ⋮ Generalized alternating hyperharmonic number sums with reciprocal binomial coefficients ⋮ Unnamed Item ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers ⋮ Efficient approximations of finite and infinite real alternating p -series ⋮ Unnamed Item ⋮ Integrals of polylogarithmic functions with alternating argument ⋮ Evaluations of sums involving harmonic numbers and binomial coefficients ⋮ Euler related binomial sums ⋮ Generalized hyperharmonic number sums with reciprocal binomial coefficients ⋮ Some evaluation of harmonic number sums ⋮ Unnamed Item ⋮ Identities for the shifted harmonic numbers and binomial coeffecients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• On generalized harmonic number sums
• The evaluation of character Euler double sums
• A note on harmonic numbers, umbral calculus and generating functions
• Integral forms of sums associated with harmonic numbers
• A formula of S. Ramanujan
• Some combinatorial series identities associated with the digamma function and harmonic numbers
• Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• Harmonic number identities via the Newton-Andrews method
• 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
• Harmonic sums and integral representations
• Harmonic number identities via hypergeometric series and Bell polynomials
• Euler Sums and Contour Integral Representations
• Values of the polygamma functions at rational arguments

This page was built for publication: Quadratic alternating harmonic number sums