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Euler sums and Stirling sums (Q1686169)

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scientific article; zbMATH DE number 6820882

Language	Label	Description	Also known as
English	Euler sums and Stirling sums	scientific article; zbMATH DE number 6820882

Statements

scholarly article

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Euler sums and Stirling sums (English)

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Journal of Number Theory

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publication date

21 December 2017

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zbMATH Keywords

Euler sums

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Stirling sums

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Bell polynomials

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generating functions

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Riemann zeta function

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MaRDI profile type

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full work available at URL

https://doi.org/10.1016/j.jnt.2017.08.037

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On Stirling numbers and Euler sums

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Experimental Evaluation of Euler Sums

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On an Intriguing Integral and Some Series Related to ζ(4)

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Explicit evaluation of Euler sums

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Consecutive evaluation of Euler sums

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Generalized harmonic numbers and Euler sums

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The Gauss<sub>2</sub><i>F</i><sub>1</sub>(1)-summation theorem and harmonic number identities

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Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function

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Explicit evaluation of Euler and related sums

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Hypergeometric series and the Riemann zeta function

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Infinite series identities on harmonic numbers

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On some log-cosine integrals related to \(\zeta(3), \zeta(4)\), and \(\zeta(6)\).

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The Arakawa-Kaneko zeta function

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Inverse binomial series and values of Arakawa-Kaneko zeta functions

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On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)

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Euler sums of hyperharmonic numbers

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Euler Sums and Contour Integral Representations

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Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums

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Series Involving Products of Two Harmonic Numbers

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Closed expressions for ∫¹₀𝑡⁻¹𝑙𝑜𝑔ⁿ⁻¹𝑡log^{𝑝}(1-𝑡)𝑑𝑡

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Nielsen’s Generalized Polylogarithms

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Harmonic number identities via hypergeometric series and Bell polynomials

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Nonlinear Euler sums

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Hyperharmonic series involving Hurwitz zeta function

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Lyndon words, polylogarithms and the Riemann \(\zeta\) function

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Computer-free evaluation of an infinite double sum via Euler sums

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Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.

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Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)

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Quadratic and cubic harmonic number sums

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A formula of S. Ramanujan

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Harmonic numbers and double binomial coefficients

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Quadratic alternating harmonic number sums

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Identities for alternating inverse squared binomial and harmonic number sums

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Identities for the harmonic numbers and binomial coefficients

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A new proof for a classical quadratic harmonic series

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Reviving the quadratic series of Au-Yeung

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Multiple zeta values and Euler sums

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Some results on Euler sums

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Tornheim type series and nonlinear Euler sums

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Euler sums and integrals of polylogarithm functions

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Explicit evaluation of quadratic Euler sums

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Some evaluation of harmonic number sums

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Further summation formulae related to generalized harmonic numbers

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1016/J.JNT.2017.08.037

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Sitelinks

Mathematics(1 entry)

mardi Publication:1686169

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