Double Euler Sums on Hurwitz Zeta Functions
Minking Eie and Wen-Chin Liaw
Source: Rocky Mountain J. Math. Volume 39, Number 6
(2009), 1869-1883.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1262271379
Digital Object Identifier: doi:10.1216/RMJ-2009-39-6-1869
Zentralblatt MATH identifier: 05652727
Mathematical Reviews number (MathSciNet): MR2575883
References
T. Aoki and Y. Ohno, Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions, Publ. RIMS Kyoto Univ. 41 (2005), 329-337.
Mathematical Reviews (MathSciNet): MR2138027
Digital Object Identifier: doi:10.2977/prims/1145475357
Zentralblatt MATH: 1081.11060
B.C. Berndt, Ramanujan's notebooks, Part I, Springer-Verlag, New York, 1985.
Mathematical Reviews (MathSciNet): MR781125
Zentralblatt MATH: 0555.10001
D. Borwein, J.M. Borwein and R. Girgensohn, Explicit evaluation of Euler sums, Proc. Edinburgh Math. Soc. 38 (1995), 277-294.
Mathematical Reviews (MathSciNet): MR1335874
Zentralblatt MATH: 0819.40003
Digital Object Identifier: doi:10.1017/S0013091500019088
J.M. Borwein, D.M. Bradley, D.J. Broadhurst and P. Lisoněk, Special values of multiple polylogarithms, Trans. Amer. Math. Soc. 353 (2001), 907-941.
Mathematical Reviews (MathSciNet): MR1709772
Zentralblatt MATH: 1002.11093
Digital Object Identifier: doi:10.1090/S0002-9947-00-02616-7
JSTOR: links.jstor.org
K.-W. Chen and M. Eie, Explicit evaluations of extended Euler sums, J. Number Theory 117 (2006), 31-52.
Mathematical Reviews (MathSciNet): MR2204734
Zentralblatt MATH: 1097.11044
Digital Object Identifier: doi:10.1016/j.jnt.2005.05.011
R.E. Crandall and J.P. Buhler, On the evaluation of Euler sums, Experiment. Math. 3 (1994), 275-285.
Mathematical Reviews (MathSciNet): MR1341720
Zentralblatt MATH: 0833.11045
Project Euclid: euclid.em/1048515810
M. Eie and W.-C. Liaw, Euler sums with Dirichlet characters, Acta Arith., to appear.
Mathematical Reviews (MathSciNet): MR2357649
Zentralblatt MATH: 1133.11049
Digital Object Identifier: doi:10.4064/aa130-2-1
M. Eie, W.-C. Liaw and Y.L. Ong, Euler sums on arithmetic progressions, New Zealand J. Math., to appear.
M. Eie, W.-C. Liaw and F.-Y. Yang, On evaluations of generalized Euler sums of even weight, Int. J. Number Theory 1 (2005), 225-242.
Mathematical Reviews (MathSciNet): MR2173382
Zentralblatt MATH: 1087.11055
Digital Object Identifier: doi:10.1142/S1793042105000182
M. Eie, Y.L. Ong and F.-Y. Yang, Evaluating double Euler sums over rationally deformed simplices, Int. J. Number Theory 1 (2005), 439-458.
Mathematical Reviews (MathSciNet): MR2175101
Zentralblatt MATH: 1114.11018
Digital Object Identifier: doi:10.1142/S1793042105000273
P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experiment. Math. 7 (1998), 15-35.
Mathematical Reviews (MathSciNet): MR1618286
Zentralblatt MATH: 0920.11061
Project Euclid: euclid.em/1047674270
M.E. Hoffman, Multiple harmonic series, Pacific J. Math. 152 (1992), 275-290.
Mathematical Reviews (MathSciNet): MR1141796
Zentralblatt MATH: 0763.11037
Project Euclid: euclid.pjm/1102636166
M.E. Hoffman and C. Moen, Sums of triple harmonic series, J. Number Theory 60 (1996), 329-331.
Mathematical Reviews (MathSciNet): MR1412967
Zentralblatt MATH: 0863.11051
Digital Object Identifier: doi:10.1006/jnth.1996.0127
C. Markett, Triple sums and the Riemann zeta function, J. Number Theory 48 (1994), 113-132.
Mathematical Reviews (MathSciNet): MR1285535
Zentralblatt MATH: 0810.11047
Digital Object Identifier: doi:10.1006/jnth.1994.1058
C.L. Siegel, Advanced analytic number theory, Tata Institute of Fundamental Research, Bombay, 1980.
Mathematical Reviews (MathSciNet): MR659851
R. Sitaramachandrarao, A formula of S. Ramanujan, J. Number Theory 25 (1987), 1-19.
Mathematical Reviews (MathSciNet): MR871165
Digital Object Identifier: doi:10.1016/0022-314X(87)90012-6
E.T. Whittaker and G.N. Watson, A course of modern analysis, 4th ed., Cambridge University Press, Cambridge, 1927. Reprinted 1996.
Mathematical Reviews (MathSciNet): MR1424469
Rocky Mountain Journal of Mathematics