单词 | Khintchine's Constant | ||||||||||||||||||||||||||||||||||||||
释义 | Khintchine's ConstantN.B. A detailed on-line essay by S. Finchwas the starting point for this entry. ![]() Let
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![]() Khintchine's constant is also given by the integral
If
![]() Define the following quantity in terms of the
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Bailey, D. H.; Borwein, J. M.; and Crandall, R. E. ``On the Khintchine Constant.'' Math. Comput. 66, 417-431, 1997. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/khntchn/khntchn.html Kac, M. Statistical Independence and Probability, Analysts and Number Theory. Providence, RI: Math. Assoc. Amer., 1959. Khinchin, A. Ya. Continued Fractions. New York: Dover, 1997. Knuth, D. E. Exercise 24 in The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 2nd ed. Reading, MA: Addison-Wesley, p. 604, 1981. Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 46, 1983. Lehmer, D. H. ``Note on an Absolute Constant of Khintchine.'' Amer. Math. Monthly 46, 148-152, 1939. Phillipp, W. ``Some Metrical Theorems in Number Theory.'' Pacific J. Math. 20, 109-127, 1967. Plouffe, S. ``Plouffe's Inverter: Table of Current Records for the Computationof Constants.'' http://www.lacim.uqam.ca/pi/records.html. Rockett, A. M. and Szüsz, P. Continued Fractions. Singapore: World Scientific, 1992. Shanks, D. and Wrench, J. W. ``Khintchine's Constant.'' Amer. Math. Monthly 66, 148-152, 1959. Sloane, N. J. A. SequencesA002210/M1564and A002211/M0118in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Vardi, I. ``Khinchin's Constant.'' §8.4 in Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 163-171, 1991. Wrench, J. W. ``Further Evaluation of Khintchine's Constant.'' Math. Comput. 14, 370-371, 1960. |
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