Symmetry and specializability in continued fractions

Henry Cohn

Acta Arithmetica (1996)

  • Volume: 75, Issue: 4, page 297-320
  • ISSN: 0065-1036

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Henry Cohn. "Symmetry and specializability in continued fractions." Acta Arithmetica 75.4 (1996): 297-320. <http://eudml.org/doc/206879>.

@article{HenryCohn1996,
author = {Henry Cohn},
journal = {Acta Arithmetica},
keywords = {continued fraction; symmetry; specializable continued fraction expansion; Chebyshev polynomials},
language = {eng},
number = {4},
pages = {297-320},
title = {Symmetry and specializability in continued fractions},
url = {http://eudml.org/doc/206879},
volume = {75},
year = {1996},
}

TY - JOUR
AU - Henry Cohn
TI - Symmetry and specializability in continued fractions
JO - Acta Arithmetica
PY - 1996
VL - 75
IS - 4
SP - 297
EP - 320
LA - eng
KW - continued fraction; symmetry; specializable continued fraction expansion; Chebyshev polynomials
UR - http://eudml.org/doc/206879
ER -

References

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  1. [1] A. Blanchard et M. Mendès France, Symétrie et transcendance, Bull. Sci. Math. 106 (1982), 325-335 
  2. [2] R. Graham, D. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, 1989. 
  3. [3] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 1979. Zbl0423.10001
  4. [4] M. Kmošek, Continued fraction expansion of some irrational numbers, Master's Thesis, Uniwersytet Warszawski, Warszawa, 1979 (in Polish). 
  5. [5] G. Köhler, Some more predictable continued fractions, Monatsh. Math. 89 (1980), 95-100. Zbl0419.10010
  6. [6] M. Mendès France, Sur les fractions continues limitées, Acta Arith. 23 (1973), 207-215. Zbl0228.10007
  7. [7] M. Mendès France and A. J. van der Poorten, Some explicit continued fraction expansions, Mathematika 38 (1991), 1-9. 
  8. [8] A. Ostrowski, Über einige Verallgemeinerungen des Eulerschen Produktes ν = 0 ( 1 + x 2 ν ) = 1 / ( 1 - x ) , Verh. Naturf. Ges. Basel 2 (1929), 153-214. 
  9. [9] A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250. Zbl0753.11005
  10. [10] A. J. van der Poorten and J. Shallit, A specialised continued fraction, Canad. J. Math. 45 (1993), 1067-1079. Zbl0797.11007
  11. [11] J. Shallit, Simple continued fractions for some irrational numbers, J. Number Theory 11 (1979), 209-217. Zbl0404.10003
  12. [12] J. Shallit, Simple continued fractions for some irrational numbers II, J. Number Theory 14 (1982), 228-231. Zbl0481.10005
  13. [13] J. Tamura, Explicit formulae for certain series representing quadratic irrationals, in: Number Theory and Combinatorics, J. Akiyama et al. (eds.), World Scientific, Singapore, 1985, 369-381. 
  14. [14] J. Tamura, Symmetric continued fractions related to certain series, J. Number Theory 38 (1991), 251-264. Zbl0734.11005

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