In this paper, we study the alternating Euler
Révisé le :
Accepté le :
Publié le :
Ce Xu 1 ; Weiping Wang 2

@article{CRMATH_2023__361_G6_979_0, author = {Ce Xu and Weiping Wang}, title = {Dirichlet type extensions of {Euler} sums}, journal = {Comptes Rendus. Math\'ematique}, pages = {979--1010}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.453}, language = {en}, }
Ce Xu; Weiping Wang. Dirichlet type extensions of Euler sums. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 979-1010. doi : 10.5802/crmath.453. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.453/
[1] Mathematica package MultipleZetaValues (2022) (https://www.researchgate.net/publication/357601353)
[2] Ramanujan’s Notebooks. Part I, Springer, 1985 | DOI
[3] Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables, Theor. Comput. Sci., Volume 273 (2002) no. 1-2, pp. 271-282 | DOI | MR | Zbl
[4] The multiple zeta value data mine, Comput. Phys., Volume 181 (2010) no. 3, pp. 582-625 | DOI | MR | Zbl
[5] Harmonic sums and Mellin transforms up to two loop order, Phys. Rev. D, Volume 60 (1999) no. 1, 014018
[6] On an intriguing integral and some series related to
[7] Explicit evaluation of Euler sums, Proc. Edinb. Math. Soc., Volume 38 (1995) no. 2, pp. 277-294 | DOI | MR | Zbl
[8] Multiple zeta values and modular forms in quantum field theory, Computer algebra in quantum field theory. Integration, summation and special functions (Texts and Monographs in Symbolic Computation), Springer, 2013, pp. 33-73 | DOI | MR | Zbl
[9] Evaluations of some variant Euler sums, J. Integer Seq., Volume 9 (2006) no. 2, 06.2.3, 9 pages | MR | Zbl
[10] Hypergeometric series and the Riemann zeta function, Acta Arith., Volume 82 (1997) no. 2, pp. 103-118 | MR | Zbl
[11] Inverse binomial series and values of Arakawa-Kaneko zeta functions, J. Number Theory, Volume 150 (2015), pp. 98-119 | DOI | MR | Zbl
[12] On some series containing
[13] Euler sums and contour integral representations, Exp. Math., Volume 7 (1998) no. 1, pp. 15-35 | DOI | MR | Zbl
[14] Multiple harmonic series, Pac. J. Math., Volume 152 (1992) no. 2, pp. 275-290 | DOI | MR | Zbl
[15] An odd variant of multiple zeta values, Commun. Number Theory Phys., Volume 13 (2019) no. 3, pp. 529-567 | DOI | MR | Zbl
[16] On multiple zeta values of level two, Tsukuba J. Math., Volume 44 (2020) no. 2, pp. 213-234 | MR | Zbl
[17] Zeta functions connecting multiple zeta values and poly-Bernoulli numbers, Various aspects of multiple zeta functions (Advanced Studies in Pure Mathematics), Volume 84, Mathematical Society of Japan, 2020, pp. 181-204 | DOI | MR | Zbl
[18] Quantum Groups, Graduate Texts in Mathematics, 155, Springer, 1995 | DOI
[19] A formula of S. Ramanujan, J. Number Theory, Volume 25 (1987) no. 1, pp. 1-19 | DOI | MR
[20] Some evaluation of parametric Euler sums, J. Math. Anal. Appl., Volume 451 (2017) no. 2, pp. 954-975 | MR | Zbl
[21] Explicit evaluations for several variants of Euler sums, Rocky Mt. J. Math., Volume 51 (2021) no. 3, pp. 1089-1106 | MR | Zbl
[22] Extensions of Euler type sums and Ramanujan type sums, Kyushu J. Math., Volume 75 (2021) no. 2, pp. 295-322 | MR | Zbl
[23] Explicit formulas of Euler sums via multiple zeta values, J. Symb. Comput., Volume 101 (2020), pp. 109-127 | MR | Zbl
[24] Two variants of Euler sums, Monatsh. Math., Volume 199 (2022) no. 2, pp. 431-454 | MR | Zbl
[25] Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II (Paris, 1992) (Progress in Mathematics), Volume 120, Birkhäuser, 1994, pp. 497-512 | DOI | MR | Zbl
[26] Multiple polylogarithm values at roots of unity, C. R. Math. Acad. Sci. Paris, Volume 346 (2008) no. 19-20, pp. 1029-1032 | DOI | Numdam | MR | Zbl
[27] Further summation formulae related to generalized harmonic numbers, J. Math. Anal. Appl., Volume 335 (2007) no. 1, pp. 692-706 | DOI | MR | Zbl
Cité par Sources :
Commentaires - Politique