Alternating multiple zeta values, and explicit formulas of some Euler–Apéry-type series
Tài liệu tham khảo
Ablinger, 2014, The package Harmonicsums: computer algebra and analytic aspects of nested sums
Ablinger, 2017, Discovering and proving infinite binomial sums identities, Exp. Math., 26, 62, 10.1080/10586458.2015.1116028
Ablinger, 2019, Discovering and proving infinite Pochhammer sum identities, Exp. Math., 10.1080/10586458.2019.1627254
Almkvist, 1999, Borwein and Bradley’s Apéry-like formulae for ζ(4n+3), Exp. Math., 8, 197, 10.1080/10586458.1999.10504398
Alzer, 2006, Series representations for some mathematical constants, J. Math. Anal. Appl., 320, 145, 10.1016/j.jmaa.2005.06.059
Apéry, 1979, Irrationalité de ζ2 et ζ3, Luminy Conference on Arithmetic, Astérisque, 61, 11
Bailey, 2006, Experimental determination of Apéry-like identities for ζ(2n+2), Exp. Math., 15, 281, 10.1080/10586458.2006.10128968
Bailey, 2007
Bailey, 1994, Experimental evaluation of Euler sums, Exp. Math., 3, 17, 10.1080/10586458.1994.10504573
Berndt, 1985
Blümlein, 2010, The multiple zeta value data mine, Comput. Phys. Commun., 181, 582, 10.1016/j.cpc.2009.11.007
Borwein, 1995, Explicit evaluation of Euler sums, Proc. Edinburgh Math. Soc. (2), 38, 277, 10.1017/S0013091500019088
Borwein, 2001, Special values of multiple polylogarithms, Trans. Amer. Math. Soc., 353, 907, 10.1090/S0002-9947-00-02616-7
Borwein, 2001, Central binomial sums, multiple Clausen values, and zeta values, Exp. Math., 10, 25, 10.1080/10586458.2001.10504426
Boyadzhiev, 2012, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq., 15
Boyadzhiev, 2017, Power series with inverse binomial coefficients and harmonic numbers, Tatra Mt. Math. Publ., 70, 199
Bradley, 2005, Multiple q-zeta values, J. Algebra, 283, 752, 10.1016/j.jalgebra.2004.09.017
Campbell, 2018, Ramanujan-like series for 1∕π involving harmonic numbers, Ramanujan J., 46, 373, 10.1007/s11139-018-9995-9
Chen, 2016, Interesting series associated with central binomial coefficients, Catalan numbers and harmonic numbers, J. Integer Seq., 19
Chen, 2017, Generalized harmonic numbers and Euler sums, Int. J. Number Theory, 13, 513, 10.1142/S1793042116500883
Chen, 2019, Generalized Arakawa–Kaneko zeta functions, Integral Transforms Spec. Funct., 30, 282, 10.1080/10652469.2018.1562450
Chu, 2017, Hypergeometric approach to Apéry-like series, Integral Transforms Spec. Funct., 28, 505, 10.1080/10652469.2017.1315416
Chu, 2009, Infinite series with harmonic numbers and central binomial coefficients, Int. J. Number Theory, 5, 429, 10.1142/S1793042109002171
Comtet, 1974
Coppo, 2015, Inverse binomial series and values of Arakawa–Kaneko zeta functions, J. Number Theory, 150, 98, 10.1016/j.jnt.2014.11.007
Davydychev, 2004, Massive Feynman diagrams and inverse binomial sums, Nuclear Phys. B, 699, 3, 10.1016/j.nuclphysb.2004.08.020
Flajolet, 1998, Euler sums and contour integral representations, Exp. Math., 7, 15, 10.1080/10586458.1998.10504356
Hessami Pilehrood, 2010, Series acceleration formulas for beta values, Discrete Math. Theor. Comput. Sci., 12, 223
Hoffman, 1992, Multiple harmonic series, Pacific J. Math., 152, 275, 10.2140/pjm.1992.152.275
Hoffman, 2017, Harmonic-number summation identities, symmetric functions, and multiple zeta values, Ramanujan J., 42, 501, 10.1007/s11139-015-9750-4
Hoffman, 2019, An odd variant of multiple zeta values, Commun. Number Theory Phys., 13, 529, 10.4310/CNTP.2019.v13.n3.a2
Jegerlehner, 2003, MS¯ vs. pole masses of gauge bosons II: two-loop electroweak fermion corrections, Nuclear Phys. B, 658, 49, 10.1016/S0550-3213(03)00177-9
Kalmykov, 2007, Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter, J. High Energy Phys., 2007, 10.1088/1126-6708/2007/10/048
Knuth, 2015, Problem 11832, Amer. Math. Monthly, 122, 390
Kuba, 2010, A note on Stirling series, Integers, 10, 393, 10.1515/integ.2010.034
Lehmer, 1985, Interesting series involving the central binomial coefficient, Amer. Math. Monthly, 92, 449, 10.1080/00029890.1985.11971651
Leshchiner, 1981, Some new identities for ζ(k), J. Number Theory, 13, 355, 10.1016/0022-314X(81)90020-2
Luke, 1969, vol. 53
Macdonald, 2015
Orr, 2019, Generalized log-sine integrals and Bell polynomials, J. Comput. Appl. Math., 347, 330, 10.1016/j.cam.2018.08.026
Riordan, 2002
Sitaramachandra Rao, 1987, A formula of S. Ramanujan, J. Number Theory, 25, 1, 10.1016/0022-314X(87)90012-6
Sprugnoli, 2006, Sums of reciprocals of the central binomial coefficients, Integers, 6
Srivastava, 2012
Sun, 2014
Sun, 2015, A new series for π3 and related congruences, Internat. J. Math., 26, 10.1142/S0129167X1550055X
Sun, 2015, New series for some special values of L-functions, Nanjing Daxue Xuebao Shuxue Bannian Kan, 32, 189
van der Poorten, 1978, A proof that Euler missed … Apéry’s proof of the irrationality of ζ(3), Math. Intell., 1, 195, 10.1007/BF03028234
Wang, 2020, Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients, Ramanujan J., 52, 641, 10.1007/s11139-019-00140-5
Wang, 2018, Euler sums and Stirling sums, J. Number Theory, 185, 160, 10.1016/j.jnt.2017.08.037
Wang, 2019
Weinzierl, 2004, Expansion around half-integer values, binomial sums, and inverse binomial sums, J. Math. Phys., 45, 2656, 10.1063/1.1758319
Xu, 2017, Multiple zeta values and Euler sums, J. Number Theory, 177, 443, 10.1016/j.jnt.2017.01.018
Xu, 2018, On harmonic numbers and nonlinear Euler sums, J. Math. Anal. Appl., 466, 1009, 10.1016/j.jmaa.2018.06.036
Xu, 2020, Explicit formulas of Euler sums via multiple zeta values, J. Symb. Comput., 101, 109, 10.1016/j.jsc.2019.06.009
Zagier, 1994, Values of zeta functions and their applications, vol. 120, 497
Zucker, 1985, On the series ∑k=1∞2kk−1k−n and related sums, J. Number Theory, 20, 92, 10.1016/0022-314X(85)90019-8