On the convergence acceleration of some continued fractions

Details On the convergence acceleration of some continued fractions On the convergence acceleration of some continued fractions

2011-08-16

arxiv.org/abs/1108.3367v2

Mathematics

Numerical Analysis

English improved

Scientific paper

A well known method for convergence acceleration of continued fraction $\K(a_n/b_n)$ is to use the modified approximants $S_n(\omega_n)$ in place of the classical approximants $S_n(0)$, where $\omega_n$ 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 $\K(a_n/b_n)$, where $a_n$, $b_n$ are polynomials in $n$ ($\deg a_n=2$, $\deg b_n\leq 1$) for sufficiently large $n$. The purpose of this paper is to extend this idea for the class of continued fractions $\K(a_n/b_n + a_n'/b_n')$, where $a_n$, $a_n'$, $b_n$, $b_n'$ are polynomials in $n$ ($\deg a_n=\deg a_n', \deg b_n=\deg b_n'$). We give examples involving such continued fraction expansions of some mathematical constants, as well as elementary and special functions.

Affiliated with

Also associated with

No associations

Rating

On the convergence acceleration of some continued fractions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the convergence acceleration of some continued fractions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the convergence acceleration of some continued fractions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539591