2011/08/16 by Rafał Nowak, Nowak, Rafał
Computer Science · Mathematics · #Advanced Mathematical Theories #History and Theory of Mathematics #Mathematics and Applications #acm:33F05 #acm:65B99 #cs.NA #math.NA #msc:33F05 #msc:65B99
paper · pdf · doi:10.48550/arxiv.1108.3367
English improved
arxiv created 2012/03/04 · arxiv updated 2012/03/06
A well known method for convergence acceleration of continued fraction \K(an/bn) is to use the modified approximants Sn(ωn) in place of the classical approximants Sn(0), where ωn are close to tails f(n) of continued fraction. Recently, author proposed a method of iterative character producing tail approximations whose asymptotic expansion's accuracy is improving in each step. This method can be applied to continued fractions \K(an/bn), where an, bn are polynomials in n (°an=2, °bn≤ 1) for sufficiently large n. The purpose of this paper is to extend this idea for the class of continued fractions \K(an/bn + an'/bn'), where an, an', bn, bn' are polynomials in n (°an=°an', °bn=°bn'). We give examples involving such continued fraction expansions of some mathematical constants, as well as elementary and special functions.