Euler sums and contour integral representations

Experimental Mathematics

Volumn 7, Issue 1, 1998, Pages 15-35

  Flajolet, Philippe ^a   Salvy, Bruno ^a  

^a INRIA ROCQUENCOURT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032219840     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.1998.10504356     Document Type: Article

References (18)

1. D. H. Bailey, J. M. Borwein, and R. Girgensohn, "Experimental evaluation of Euler sums", Experiment. Math., 3, 1 (1994), 17-30.
2. B. C. Berndt, Ramanujan's notebooks, II, Springer, New York, 1985. With a foreword by S. Chandrasekhar.
3. B. C. Berndt, Ramanujan's notebooks, I, Springer, New York, 1989.
4. J. M. Borwein and R. Girgensohn, "Evaluation of triple Euler sums", Electron. J. Combin., 3, 1 (1996), Research Paper 23, 27 pp. (electronic).
5. D. Borwein, J. M. Borwein, and R. Girgensohn, "Explicit evaluation of Euler sums", Proc. Edinburgh Math. Soc. (2), 38, 2 (1995), 277-294.
6. R. E. Crandall and J. P. Buhler, "On the evaluation of Euler sums", Experiment. Math., 3, 4 (1994), 275-285.
7. H. Daude, P. Flajolet, and B. Vallee, "An average-case analysis of the Gaussian algorithm for lattice reduction", Combinatorics, Probability, and Computing, 6, 4 (1997), 397-433.
8. 2 for certain values of x and y", J. Comput. Appl. Math., 37, 1-3 (1991), 125-141.
9. P. Flajolet, G. Labelle, L. Laforest, and B. Salvy, "Hypergeometrics and the cost structure of quadtrees", Random Structures Algorithms, 7, 2 (1995), 117-144.
10. P. Henrici, Applied and computational complex analysis, Pure and Applied Mathematics, Wiley-Interscience, New York, 1974. Reprinted 1988.
11. M. E. Hoffman, "Multiple harmonic series", Pacific J. Math., 152, 2 (1992), 275-290
12. G. Labelle and L. Laforest, "Combinatorial variations on multidimensional quadtrees", J. Combin. Theory Ser. A, 69, 1 (1995), 1-16.
13. E. Lindelof, Le calcul des residua et ses applications Ii la theorie des fonctions, GauthierVillars, Paris, 1905. Reprinted by Editions Jacques Gabay, Sceaux, 1989.
14. C. Markett, "Triple sums and the Riemann zeta function", J. Number Theory, 48, 2 (1994), 113-132.
15. N. Nielsen, Handbuch der Theorie der Gammafunktion and Theorie des Integrallogarithmua und ueruumdier Transzendenten, 1906. Reprinted together as Die Gammafunktion, Chelsea, New York, 1965.
16. R. Sitaramachandra Rao, "A formula of S. Ramanujan", J. Number Theory, 25, 1 (1987), 1-19.
17. E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1927. Reprinted 1973, 1996.
18. D. Zagier, "Values of zeta functions and their applications", pp. 497-512 in First European Congress of Mathematics (Paris, 1992), vol. II, edited by A. Joseph et al., Progr. Math., 120, Birkhauser, Basel, 1994.