Gauss-Kuzmin-Wirsing Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Let 
be a random number from 
written as a simple Continued Fraction
 | (1) |
 |  |  | |
|  | (2) |
Gauß
(1800) showed that if 
is the probability that 
, then | (3) |
 | (4) |
and 
is an analytic function with 
This constant is connected to the efficiency of the Euclidean Algorithm (Knuth 1981).
References
Babenko, K. I. ``On a Problem of Gauss.'' Soviet Math. Dokl. 19, 136-140, 1978. Daudé, H.; Flajolet, P.; and Vallée, B. ``An Average-Case Analysis of the Gaussian Algorithm for Lattice Reduction.'' Submitted. Durner, A. ``On a Theorem of Gauss-Kuzmin-Lévy.'' Arch. Math. 58, 251-256, 1992. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/kuzmin/kuzmin.html Flajolet, P. and Vallée, B. ``On the Gauss-Kuzmin-Wirsing Constant.'' Unpublished memo. 1995. http://pauillac.inria.fr/algo/flajolet/Publications/gauss-kuzmin.ps. Knuth, D. E. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1981. MacLeod, A. J. ``High-Accuracy Numerical Values of the Gauss-Kuzmin Continued Fraction Problem.'' Computers Math. Appl. 26, 37-44, 1993. Wirsing, E. ``On the Theorem of Gauss-Kuzmin-Lévy and a Frobenius-Type Theorem for Function Spaces.'' Acta Arith. 24, 507-528, 1974.
- Different Prime Factors
- Digamma Function
- Digimetic
- Digit
- Digitaddition
- Digital Root
- Digon
- Digraph
- Dihedral Angle
- Dihedral Group
- Dijkstra's Algorithm
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- Dilworth's Lemma
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- Dimension
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- Diminished Polyhedron
- Diminished Rhombicosidodecahedron
- Dini Expansion
- Dini's Surface