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Original Articles

On the Random Character of Fundamental Constant Expansions

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Pages 175-190 | Published online: 04 Apr 2012

REFERENCES

  • Adamchik , V. and Wagon , S. 1997 . “A simple formula for π” . Amer. Math. Monthly , 104 ( 9 ) : 852 – 855 . [Adamchik and Wagon 1997]
  • Bailey , D. H. and Crandall , R. E. 2001 . “Random generators and normal numbers” [Bailey and Crandall 2001], preprint
  • Bailey , D. , Borwein , P. and Plouffe , S. 1997 . “On the rapid computation of various polylogarithmic constants” . Math. Comp. , 66 ( 218 ) : 903 – 913 . [Bailey et al. 1997]
  • Beeler , M. , Gosper , R. W. and Schroeppel , R. 1972 . “HAKMEM” Cambridge , MA : Mass. Inst. Technology AI Lab. . [Beeler et al. 1972], Memo AIM-239
  • Borwein , J. M. , Bradley , D. M. and Crandall , R. E. 2000 . “Computational strategies for the Riemann zeta function” . J. Comput. Appl. Math. , 121 ( 1–2 ) : 247 – 296 . [Borwein et al. 2000], http://www.cecm.sfu.ca/preprints/1998pp.htmlSee
  • Broadhurst , D. J. 1998 . “Polylogarithmic ladders, hypergeometric series and the ten millionth digits of ζ(3) and ζ(5)” [Broadhurst 1998], http://arxiv.org/abs/math/9803067Seepreprint
  • Broadhurst , D. J. 1999 . “Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity” . Eur. Phys. J. C Part. Fields , 8 ( 2 ) : 313 – 333 . [Broadhurst 1999], http://arxiv.org/abs/hep-th/9803091See
  • Broadhurst , D. J. 2000 . “Conjecture on integer-base polylogarithmic zeros motivated by the Cunningham project” [Broadhurst 2000], preprint
  • Cassels , J. W. S. 1959 . “On a problem of Steinhaus about normal numbers” . Colloq. Math. , 7 : 95 – 101 . [Cassels 1959]
  • Champernowne , D. G. 1933 . “The construction of decimals normal in the scale of ten” . J. London Math. Soc. , 8 : 254 – 260 . [Champernowne 1933]
  • Copeland , A. H. and Erdös , P. 1946 . “Note on normal numbers” . Bull. Amer. Math. Soc. , 52 : 857 – 860 . [Copeland and Erdös 1946]
  • Crandall , R. E. 1996 . Topics in advanced scientific computation New York : Springer. . [Crandall 1996]
  • Ferguson , H. R. P. , Bailey , D. H. and Arno , S. 1999 . “Analysis of PSLQ, an integer relation finding algorithm” . Math. Comp. , 68 ( 225 ) : 351 – 369 . [Ferguson et al. 1999]
  • Kuipers , L. and Niederreiter , H. 1974 . Uniform distribution of sequences New York : Wiley-Interscience. . [Kuipers and Niederreiter 1974]
  • Lagarias , J. C. 2001 . “On the normality of fundamental constants” . Experiment. Math. , 10 ( 2 ) [Lagarias 2001]
  • Martin , G. 2000 . “Absolutely abnormal numbers” [Martin 2000], http://arxiv.org/abs/math/0006089/preprint, See
  • Niven , I. 1956 . Irrational numbers New York : Math. Assoc. of America and Wiley. . [Niven 1956]
  • Percival , C. 2000 . “The quadrillionth bit of pi is ‘0’” [Percival 2000], http://cecm.sfu.ca/pihex/announcelq.htmlpreprint, See

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