Explicit evaluation of Euler and related sums

DOI10.1007/s11139-005-3505-6zbMath1115.11052OpenAlexW2094244930MaRDI QIDQ850508

Junesang Choi, Hari M. Srivastava

Publication date: 3 November 2006

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-005-3505-6

zbMATH Keywords

gamma functionhypergeometric seriesEuler sumsPsi functionpolylogarithm functionspolygamma functionsStirling numbers of the first kindRiemann Zeta functionGauss summation theorem(generalized) harmonic numbersHurwitz Zeta functionrecurrence relations and recursion formulasTaylor-Maclaurin series

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) Generalized hypergeometric series, ({}_pF_q) (33C20) Hurwitz and Lerch zeta functions (11M35)

Related Items (31)

Harmonic number identities via hypergeometric series and Bell polynomials ⋮ Evaluation of series involving the product of the tail of \(\zeta(k)\) and \(\zeta(k+1)\) ⋮ Explicit identities for infinite families of series involving squared binomial coefficients ⋮ Further summation formulae related to generalized harmonic numbers ⋮ Extension of the four Euler sums being linear with parameters and series involving the zeta functions ⋮ Identities for Reciprocal Binomials ⋮ Infinite summation formulas related to Riemann Zeta function from hypergeometric series ⋮ Euler sums and Stirling sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Some summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum ⋮ Euler sums of generalized harmonic numbers and connected extensions ⋮ A new class of identities involving Cauchy numbers, harmonic numbers and zeta values ⋮ Generalized harmonic numbers and Euler sums ⋮ Computation of the Mordell-Tornheim zeta values ⋮ Certain summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers ⋮ Reviving the quadratic series of Au-Yeung ⋮ Harmonic series with polygamma functions ⋮ Evaluation of a cubic Euler sum ⋮ Inverse binomial series and values of Arakawa-Kaneko zeta functions ⋮ Identities for the harmonic numbers and binomial coefficients ⋮ Four parametric linear Euler sums ⋮ Evaluations of some classes of the trigonometric moment integrals ⋮ Explicit formulas of sums involving harmonic numbers and Stirling numbers ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers ⋮ On some combinatorial identities and harmonic sums ⋮ Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals ⋮ Quadratic series involving the tail of ζ(k) ⋮ Multinomial coefficients, multiple zeta values, Euler sums and series of powers of the Hurwitz zeta function ⋮ Unnamed Item

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