Experimental Evaluation of Euler Sums

REFERENCES

• Abramowitz , M. and Stegun , I. A. 1972 . Handbook of Mathematical Functions New York : Dover. . [Abramowitz and Stegun 1972]
   Google Scholar
• Atkinson , K. E. 1989 . An Introduction to Numerical Analysis New York : Wiley. . [Atkinson 1989]
   Google Scholar
• Bailey , D. H. “Multiprecision translation and execution of Fortran programs,”. ” . In ACM Transactions on Mathematical Software [Bailey], to appear. This software and documentation may be obtained by sending electronic mail to mp-requestφnas. nasa. gov.
   Google Scholar
• Bailey , D. H. and Ferguson , H. R. P. 1989 . “Numerical results on relations between numerical constants using a new algorithm,” . Math. Comp. , 53 : 649 – 656 . [Bailey and Ferguson 1989]
   Web of Science ®Google Scholar
• Berndt , B. C. 1985 . Ramanujan's Notebook New York : Springer. . [Berndt 1985], Part I
   Google Scholar
• Borwein , D. and Borwein , J. M. “On an intriguing integral and some series related to ζ(4),” [Borwein and Borwein 1994], to appear in Proc. Amer. Math. Soc
   Google Scholar
• Borwein , D. , Borwein , J. M. and Girgensohn , R. “Explicit evaluation of Euler sums,” [Borwein et al. 1994], to appear in Proc. Edinburgh Math. Soc.
   Google Scholar
• Borwein , J. M. and Borwein , P. B. 1987 . Pi and the AGM New York : Wiley. . [Borwein and Borwein 1987]
   Google Scholar
• Borwein , J. M. , Borwein , P. B. and Dilcher , K. 1989 . “Pi, Euler Numbers and Asymptotic Expansions,” . Amer. Math. Monthly , 96 : 681 – 687 . [Borwein et al. 1989]
   Web of Science ®Google Scholar
• Char , B. W. , Geddes , K. O. , Gonnet , G. H. , Leong , B. L. , Monagan , M. B. and Watt , S. M. 1991 . Maple V Language Reference Manual New York : Springer. . [Char et al. 1991]
   Google Scholar
• De Doelder , P. J. 1991 . “On some series containing ψ()–ψ() and (ψ()–p()) for certain values of and,” . J. Comp. Appl. Math. , 37 : 125 – 141 . [De Doelder 1991]
   Web of Science ®Google Scholar
• Ferguson , H. R. P. and Bailey , D. H. “A polynomial time, numerically stable integer relation algorithm,” Moffett Field , CA : NASA Ames Research Center. . [Ferguson and Bailey 1991], RNR Technical Report RNR-91–032, MS T045–1, 94035–1000
   Google Scholar
• Ferguson , H. R. P. and Forcade , R. W. 1979 . “Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two,” . Bull. Amer. Math. Soc. , : 912 – 914 . [Ferguson and Forcade 1979]
   Web of Science ®Google Scholar
• Ferguson , H. R. P. 1987 . “A non-inductive GL(n, z) algorithm that constructs linear relations for z-linearly dependent real numbers,” . J. Algorithms , : 131 – 145 . [Ferguson 1987]
   Google Scholar
• Hastad , J. , Just , B. , Lagarias , J. C. and Schnorr , C. P. 1988 . “Polynomial time algorithms for finding integer relations among real numbers,” . SIAM J. Computing , 18 : 859 – 881 . [Hastad et al. 1988]
   Web of Science ®Google Scholar
• Knuth , D. E. 1973 . The Art of Computer Programming vol. 1 , Reading , MA : Addison-Wesley. . [Knuth 1973]
   Google Scholar
• Knuth , D. E. 1981 . The Art of Computer Programming vol. 2 , Reading , MA : Addison-Wesley. . [Knuth 1981]
   Google Scholar
• Lenstra , A. K. , Lenstra , H. W. and Lovasz , L. 1982 . “Factoring polynomials with rational coefficients” . Math. Annalen , 261 : 515 – 534 . [Lenstra et al. 1982]
   Web of Science ®Google Scholar
• Lewin , L. 1981 . Polylogarithms and associated functions New York : North-Holland. . [Lewin 1981]
   Google Scholar
• Wolfram , S. 1991 . Mathematical A System for Doing Mathematics by Computer, , 2nd ed. Reading , MA : Addison-Wesley. . [Wolfram 1991]
   Google Scholar