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2012, University lecture series, ISBN 9780821853672, Volume 59, x, 190
Book
Pacific Journal of Mathematics, ISSN 0030-8730, 2014, Volume 272, Issue 1, pp. 201 - 226
We work out some formulas for nonlinear Euler sums involving multiple zeta values. As applications of these formulas, we give new closed form sums of several... 
Euler sums | Multiple zeta values | Polygamma functions | Polylogarithm functions | Nonlinear Euler sums | Landen's identities | INTEGRALS | MATHEMATICS | nonlinear Euler sums | SERIES | multiple zeta values | RIEMANN ZETA-FUNCTION | STIRLING NUMBERS | VALUES | polygamma functions | polylogarithm functions
Journal Article
Journal of Number Theory, ISSN 0022-314X, 11/2017, Volume 180, pp. 310 - 348
For any positive integers k and j, we consider some asymptotic formulas for weighted averages of the Cohen–Ramanujan sums sk(s)(j)=∑d|k,ds|jf(d)g(kd) with any... 
Asymptotic results on arithmetical functions | Euler totient function | Bernoulli polynomials | Ramanujan sums | Gamma function | gcd-sum functions | Dedekind totient function | MATHEMATICS | functions | EXTENSION | VALUES | Asymptotic results on arithmetical
Journal Article
by Xu, Ce
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 789 - 805
P. Flajolet and B. Salvy [15] prove the famous theorem that a nonlinear Euler sum Si1i2⋯ir,q reduces to a combination of sums of lower orders whenever the... 
Euler sum | Riemann zeta function | Polylogarithm function | Harmonic number | Tornheim type series | Multiple zeta value | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | Ricmann zeta function | VALUES | Euler sure | EXPLICIT EVALUATION
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 1009 - 1042
In this paper we are interested in Euler-type sums with products of harmonic numbers, Stirling numbers and Bell numbers. We discuss the analytic... 
Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES
Journal Article
Journal of Number Theory, ISSN 0022-314X, 07/2017, Volume 176, pp. 449 - 472
Let gcd⁡(k,j) be the greatest common divisor of the integers k and j. We establish some asymptotic formulas for weighted averages of the gcd-sum functions,... 
Euler totient function | Asymptotic results on arithmetical functions | gcd-sum functions | Dedekind function | Anderson–Apostol sums | Dirichlet divisor problem | MATHEMATICS | Anderson-Apostol sums
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 419 - 434
This paper develops an approach to evaluation of Euler related sums. The approach is based on simple integral computations. By the approach, we can obtain some... 
Euler sums | Riemann zeta function | Polylogarithm function | Harmonic numbers | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | Rieman zeta function
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2016, Volume 165, pp. 84 - 108
This paper develops an approach to evaluation of Euler sums and integrals of polylogarithm functions. The approach is based on simple Cauchy product formula... 
Euler sums | Riemann zeta function | Polylogarithm functions | MATHEMATICS
Journal Article
by Xu, Ce
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2017, Volume 451, Issue 2, pp. 954 - 975
In this paper, by using the method of Contour Integral Representations and the Theorem of Residues and integral representations of series, we discuss the... 
Euler sum | Riemann zeta function | Harmonic number | Hurwitz zeta function | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2017, Volume 40, Issue 7, pp. 2347 - 2361
Journal Article
by Xu, Ce
Journal of Number Theory, ISSN 0022-314X, 08/2017, Volume 177, pp. 443 - 478
In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and... 
Multiple star harmonic number | Euler sum | Multiple zeta star value | Multiple zeta value | Multiple harmonic number | INTEGRALS | MATHEMATICS | SERIES | NUMBERS | DUALITY | FORMULAS | RIEMANN ZETA | Mathematics - Number Theory
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2019, Volume 42, Issue 4, pp. 1082 - 1098
Recently, several works are done on the generalized Dedekind‐Vasyunin sum Capq=−qa∑k=1q−1ζ−a,kpqcotπkq, where a∈C,p and q are positive coprime integers, and... 
fractional part function | Dedekind‐Vasyunin‐cotangent sum | Riemann hypothesis | Dedekind-Vasyunin-cotangent sum | MATHEMATICS, APPLIED | EULER | Integers | Reciprocity
Journal Article
Journal of Number Theory, ISSN 0022-314X, 05/2017, Volume 174, pp. 40 - 67
In this paper, we develop an approach to evaluation of nonlinear Euler sums. The approach is based on Tornheim type series computations. By the approach, we... 
Euler sums | Riemann zeta function | Polylogarithm function | Tornheim type series | Harmonic numbers | INTEGRALS | MATHEMATICS
Journal Article
Annual Review of Physical Chemistry, ISSN 0066-426X, 4/2015, Volume 66, Issue 1, pp. 189 - 216
Journal Article
by Xu, Ce
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 346, pp. 594 - 611
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral... 
Euler sum | Riemann zeta function | Multiple zeta (star) value | Multiple harmonic (star) sum | polylogarithm function | Harmonic number | INTEGRALS | MATHEMATICS, APPLIED | MULTIPLE ZETA VALUES
Journal Article
by Xu, C
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, 01/2020, Volume 43, Issue 1, pp. 847 - 877
Let p, p(1),..., p(m) be positive integers with p(1) <= p(2) <= center dot center dot center dot <= p(m) and x is an element of [-1, 1), define the so-called... 
MATHEMATICS | Polylogarithm function | IDENTITIES | Harmonic number | Multiple harmonic sum | Euler sum | Riemann zeta function | Multiple zeta value | EXPLICIT EVALUATION | MULTIPLE ZETA VALUES
Journal Article