HIGH-ACCURACY NUMERICAL VALUES IN THE GAUSS-KUZMIN CONTINUED-FRACTIONPROBLEM

Authors
Citation
Aj. Macleod, HIGH-ACCURACY NUMERICAL VALUES IN THE GAUSS-KUZMIN CONTINUED-FRACTIONPROBLEM, Computers & mathematics with applications, 26(3), 1993, pp. 37-44
Citations number
8
Categorie Soggetti
Computer Sciences",Mathematics,"Computer Applications & Cybernetics
ISSN journal
08981221
Volume
26
Issue
3
Year of publication
1993
Pages
37 - 44
Database
ISI
SICI code
0898-1221(1993)26:3<37:HNVITG>2.0.ZU;2-6
Abstract
If xepsilon[0, 1], we can expand x in a regular continued fraction x = 1/(a1 + 1/(a2 + 1/(a3 + ...))). The integers a(i), i = 1,... can be g enerated by the recursion a(i) = int (1/x(i-1)), x(i) = 1/x(i-1) - a(i ), i = 1,..., with x0 = x. If x is uniformly distributed in [0, 1], de fine F(n)(x) = Prob (x(n) < x). Babenko showed F(n)(x) = ln(1 + x)/ln 2 + SIGMA(k=2)infinity lambda(k)(n)B(k)(x). In this work, we report ve ry high accuracy values for lambda2 to lambda10, together with 10D Che byshev coefficients for B2 to B-10. Simulation results suggest that th ese values give very accurate approximations.