Explicit formulas of Euler sums via multiple zeta values
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Publication:2188978
DOI10.1016/j.jsc.2019.06.009zbMath1459.11173arXiv1805.08056OpenAlexW2964142885MaRDI QIDQ2188978
Publication date: 15 June 2020
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.08056
Special sequences and polynomials (11B83) Approximation to limiting values (summation of series, etc.) (40A25) Multiple Dirichlet series and zeta functions and multizeta values (11M32)
Related Items (13)
Euler-type sums involving multiple harmonic sums and binomial coefficients ⋮ Two variants of Euler sums ⋮ On variants of the Euler sums and symmetric extensions of the Kaneko-Tsumura conjecture ⋮ Dirichlet type extensions of Euler sums ⋮ Unnamed Item ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ Explicit evaluations for several variants of Euler sums ⋮ Explicit formulas of some mixed Euler sums via alternating multiple zeta values ⋮ Explicit formulas of sums involving harmonic numbers and Stirling numbers ⋮ On evaluations of Euler-type sums of hyperharmonic numbers ⋮ On some explicit evaluations of nonlinear Euler sums ⋮ Double shuffle relations for arborified zeta values ⋮ EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS
Uses Software
Cites Work
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- Euler sums and integrals of polylogarithm functions
- Nonlinear Euler sums
- Tornheim type series and nonlinear Euler sums
- Multiple zeta values and Euler sums
- The multiple zeta value data mine
- On Stirling numbers and Euler sums
- XSummer -- transcendental functions and symbolic summation in form
- Computer-free evaluation of an infinite double sum via Euler sums
- Explicit evaluation of Euler and related sums
- A formula of S. Ramanujan
- On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
- Multiple harmonic series
- The algebra of multiple harmonic series
- Evaluations of \(k\)-fold Euler/Zagier sums: a compendium of results for arbitrary \(k\)
- Evaluation of triple Euler sums
- On some log-cosine integrals related to \(\zeta(3), \zeta(4)\), and \(\zeta(6)\).
- Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables
- Consecutive evaluation of Euler sums
- Some evaluation of cubic Euler sums
- On harmonic numbers and nonlinear Euler sums
- Euler sums and Stirling sums
- Some results on Euler sums
- Alternating double Euler sums, hypergeometric identities and a theorem of Zagier
- Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
- Lyndon words, polylogarithms and the Riemann \(\zeta\) function
- Further summation formulae related to generalized harmonic numbers
- Series Involving Products of Two Harmonic Numbers
- Generalized harmonic numbers and Euler sums
- Explicit evaluation of quadratic Euler sums
- Closed expressions for ∫¹₀𝑡⁻¹𝑙𝑜𝑔ⁿ⁻¹𝑡log^{𝑝}(1-𝑡)𝑑𝑡
- The Gauss2F1(1)-summation theorem and harmonic number identities
- Nielsen’s Generalized Polylogarithms
- Euler Sums and Contour Integral Representations
- HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
- Experimental Evaluation of Euler Sums
- Hypergeometric series and the Riemann zeta function
- Explicit evaluation of harmonic sums
- Reviving the quadratic series of Au-Yeung
- A new proof for a classical quadratic harmonic series
- Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
- Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
- Explicit evaluation of Euler sums
- On an Intriguing Integral and Some Series Related to ζ(4)
- Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
- Multiple Zeta Values and Modular Forms in Quantum Field Theory
- New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series
- The Arakawa-Kaneko zeta function
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