Symmetry and specializability in continued fractions

Henry Cohn

ArticleOriginal scientific text

Title

Symmetry and specializability in continued fractions

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Affiliations

Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, U.S.A.

A. Blanchard et M. Mendès France, Symétrie et transcendance, Bull. Sci. Math. 106 (1982), 325-335
R. Graham, D. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, 1989.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 1979.
M. Kmošek, Continued fraction expansion of some irrational numbers, Master's Thesis, Uniwersytet Warszawski, Warszawa, 1979 (in Polish).
G. Köhler, Some more predictable continued fractions, Monatsh. Math. 89 (1980), 95-100.
M. Mendès France, Sur les fractions continues limitées, Acta Arith. 23 (1973), 207-215.
M. Mendès France and A. J. van der Poorten, Some explicit continued fraction expansions, Mathematika 38 (1991), 1-9.
A. Ostrowski, Über einige Verallgemeinerungen des Eulerschen Produktes $\prod^{\infty}_{ν = 0} (1 + x^{2^{ν}}) = \frac{1}{1 - x}$ , Verh. Naturf. Ges. Basel 2 (1929), 153-214.
A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250.
A. J. van der Poorten and J. Shallit, A specialised continued fraction, Canad. J. Math. 45 (1993), 1067-1079.
J. Shallit, Simple continued fractions for some irrational numbers, J. Number Theory 11 (1979), 209-217.
J. Shallit, Simple continued fractions for some irrational numbers II, J. Number Theory 14 (1982), 228-231.
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.
J. Tamura, Symmetric continued fractions related to certain series, J. Number Theory 38 (1991), 251-264.

Title

Symmetry and specializability in continued fractions

Affiliations

Bibliography