A Gauss-Kusmin Theorem for Optimal Continued Fractions

@misc{citeulike:408009, abstract = {this paper is to obtain a Gauss-Kusmin theorem for the OCF. To be more precise, we will show \Gamma among many other things \Gamma that for z 2 [\Gamma ; g] () f 2 [\Gamma 1 2 zg = ([\Gamma 1 ; g) with density d (x), given by (x) = ? ? ? ? ? ? ! ? ? ? ? ? ? 2x+1 2x 2 +2x+1 if \Gamma 2 x ! \Gammag log G x+1 +2x+2 if \Gamma g x ! 3 1\Gammax\Gammax (x +2x+2)(2x \Gamma2x+1) if 2 x ! g; (8) and where T is given by = [ 0; \" n+1 b n+1 ; \" n+2 b...}, author = {And, Karma D. }, citeulike-article-id = {408009}, keywords = {continued, fractions, gauss-kusmin, optimal, theorem}, posted-at = {2005-11-25 10:46:06}, priority = {2}, title = {A Gauss-Kusmin Theorem for Optimal Continued Fractions}, url = {http://citeseer.ist.psu.edu/562617.html} }

TY - GEN ID - citeulike:408009 L3 - citeulike-article-id:408009 TI - A Gauss-Kusmin Theorem for Optimal Continued Fractions N2 - this paper is to obtain a Gauss-Kusmin theorem for the OCF. To be more precise, we will show \Gamma among many other things \Gamma that for z 2 [\Gamma ; g] () f 2 [\Gamma 1 2 zg = ([\Gamma 1 ; g) with density d (x), given by (x) = ? ? ? ? ? ? ! ? ? ? ? ? ? 2x+1 2x 2 +2x+1 if \Gamma 2 x ! \Gammag log G x+1 +2x+2 if \Gamma g x ! 3 1\Gammax\Gammax (x +2x+2)(2x \Gamma2x+1) if 2 x ! g; (8) and where T is given by = [ 0; " n+1 b n+1 ; " n+2 b... KW - continued KW - fractions KW - gauss-kusmin KW - optimal KW - theorem AU - And, Karma UR - http://citeseer.ist.psu.edu/562617.html ER -