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- W1959191307 abstract "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 $n$ ($deg a_n=2$, $deg b_nleq 1$) 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." @default.
- W1959191307 created "2016-06-24" @default.
- W1959191307 creator A5078521821 @default.
- W1959191307 date "2011-08-16" @default.
- W1959191307 modified "2023-09-27" @default.
- W1959191307 title "On the convergence acceleration of some continued fractions" @default.
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