Euler Sums and Contour Integral Representations

DOI10.1080/10586458.1998.10504356zbMath0920.11061OpenAlexW2083779556MaRDI QIDQ4228034

Publication date: 10 September 1999

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/223587

zbMATH Keywords

survey Euler sums contour integral representations alternating Euler sums

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items

Alternating double $t$-values and $T$-values, Euler sums and integrals of polylogarithm functions, A simple observation on decomposition of multiple zeta values, Integrals of inverse trigonometric and polylogarithmic functions, Identities for alternating inverse squared binomial and harmonic number sums, Unnamed Item, Explicit evaluation of Euler and related sums, Some evaluation of cubic Euler sums, On harmonic numbers and nonlinear Euler sums, Further summation formulae related to generalized harmonic numbers, Extension of the four Euler sums being linear with parameters and series involving the zeta functions, Euler sums of generalized hyperharmonic numbers, Quadratic and cubic harmonic number sums, Log-hyperbolic tangent integrals and Euler sums, Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions, Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results, Generalization of harmonic sums involving inverse binomial coefficients, Two variants of Euler sums, Generalization of the non-local derangement identity and applications to multiple zeta-type series, Some evaluation of parametric Euler sums, Correction to: ``A de Bruijn-Erdős theorem in graphs?, Sum relations from shuffle products of alternating multiple zeta values, Euler sums and Stirling sums, Explicit formulas of Euler sums via multiple zeta values, New multiple harmonic sum identities, Values of the Riemann zeta function and the Dirichlet beta function at positive integer points and multiple numerical series, Generating functions for multiple zeta star values, Evaluations of some quadruple Euler sums of even weight, Identities on harmonic and $q$-harmonic number sums, Generalized harmonic numbers and Euler sums, Signed $q$-analogs of Tornheim's double series, Explicit evaluation of quadratic Euler sums, Theory and computation of Euler sums of generalized hyperharmonic numbers, Generalized harmonic number sums and quasisymmetric functions, On some log-cosine integrals related to $\zeta(3), \zeta(4)$, and $\zeta(6)$., Harmonic number identities via polynomials with $r$-Lah coefficients, Some results on $q$-harmonic number sums, The box parameter for words and permutations, Integrals involving the Legendre Chi function, A stochastically quasi-optimal search algorithm for the maximum of the simple random walk, On $q$-analogues of quadratic Euler sums, Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers, Euler sums of hyperharmonic numbers, Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series, Half-integer values of the sums of harmonic numbers of order two, Harmonic numbers and cubed binomial coefficients, Integrals of polylogarithmic functions with negative argument, Two integrals involving the Legendre chi function, New families of alternating harmonic number sums, Explicit evaluations for several variants of Euler sums, Euler sums of generalized alternating hyperharmonic numbers, Identities for the multiple zeta (star) values, Tornheim type series and nonlinear Euler sums, Some results on Euler sums, On Stirling numbers and Euler sums, General order Euler sums with multiple argument, Explicit evaluations of sums of sequence tails, Harmonic-number summation identities, symmetric functions, and multiple zeta values, Some evaluation of infinite series involving trigonometric and hyperbolic functions, Some evaluation of $q$-analogues of Euler sums, Alternating double Euler sums, hypergeometric identities and a theorem of Zagier, Special values of generalized polylogarithms, Multiple zeta values and Euler sums, Identities for the harmonic numbers and binomial coefficients, Explicit formulas of some mixed Euler sums via alternating multiple zeta values, On $q$-analogues of double Euler sums, Evaluations of nonlinear Euler sums of weight ten, On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams, On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums, Explicit evaluations of extended Euler sums, Summation formula involving harmonic numbers, Structural theorems for symbolic summation, On the Normality of Arithmetical Constants, On generalized harmonic number sums, Ramanujan summation and the exponential generating function $\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\zeta'(-k)$, Integral Representation and Algorithms for Closed Form Summation, Structure of polyzetas and Lyndon words, Four parametric linear Euler sums, EVALUATING DOUBLE EULER SUMS OVER RATIONALLY DEFORMED SIMPLICES, Integral representations of functions and Addison-type series for mathematical constants, Symmetries of Bernoulli polynomial series and Arakawa-Kaneko zeta functions, On recurrence relations for the extensions of Euler sums, Harmonic numbers at half integer values, Generalized alternating hyperharmonic number sums with reciprocal binomial coefficients, Evaluations of Euler-type sums of weight $\le 5$, Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers, EVALUATING LOG-TANGENT INTEGRALS VIA EULER SUMS, On evaluations of Euler-type sums of hyperharmonic numbers, On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions, Multinomial coefficients, multiple zeta values, Euler sums and series of powers of the Hurwitz zeta function, Double Euler sums on Hurwitz zeta functions, Generalized hyperharmonic number sums with reciprocal binomial coefficients, On the variance of the number of maxima in random vectors and its applications, Hyperharmonic series involving Hurwitz zeta function, On some explicit evaluations of nonlinear Euler sums, Evaluations of some Euler-Apéry-type series, On convergent series representations of Mellin-Barnes integrals, Quadratic alternating harmonic number sums, Double weighted sum formulas of multiple zeta values, Variants of multiple zeta values with even and odd summation indices, Special values of multiple polylogarithms, Some evaluations of parametric Euler type sums of harmonic numbers, Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers, Variant Alternating Euler Sums of Higher Order, THIRTY-TWO GOLDBACH VARIATIONS, Some BBP-type series for polylog integrals, Explicit evaluation of some integrals involving polylogarithm functions, The representation of Euler sums with parameters, Parameterized families of polylog integrals, Integrals of polylogarithms and infinite series involving generalized harmonic numbers, On variants of the Euler sums and symmetric extensions of the Kaneko-Tsumura conjecture, Dirichlet type extensions of Euler sums, Philippe Flajolet's early work in combinatorics, Evaluation of and period polynomial relations, In the shadow of Euler's greatness: adventures in the rediscovery of an intriguing sum, Euler sums of generalized hyperharmonic numbers, Unnamed Item, The representation of the generalized linear Euler sums with parameters, Sums of quadratic half integer harmonic numbers of alternating type, A new proof for a classical quadratic harmonic series, New results containing quadratic harmonic numbers, A master theorem of series and an evaluation of a cubic harmonic series, ON EVALUATION OF GENERALIZED EULER SUMS OF EVEN WEIGHT, Evaluation of Euler-like sums via Hurwitz zeta values, Maxima in hypercubes, Alternating cubic Euler sums with binomial squared terms, On representation problems of Euler sums with multi-parameters, Mixed binomial sum identities, New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series, Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums, Explicit evaluation of harmonic sums, SOME EXPLICIT PROPERTIES OF (p, q)-ANALOGUE EULER SUM USING (p, q)-SPECIAL POLYNOMIALS, EXPLICIT EVALUATION OF TRIPLE EULER SUMS, General order Euler sums with rational argument, New interesting Euler sums, Explicit formulas of sums involving harmonic numbers and Stirling numbers, On some combinatorial identities and harmonic sums, Some evaluations of infinite series involving parametric harmonic numbers, Integrals of polylogarithmic functions with alternating argument, Evaluations of sums involving harmonic numbers and binomial coefficients, Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals, Some evaluation of harmonic number sums, Identities for the shifted harmonic numbers and binomial coeffecients, A two-variable Dirichlet series and its applications, Symbolic computations via Fourier–Legendre expansions and fractional operators, EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS

Cites Work