A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals
A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals
复制标题
$e^{1/s}$ 在积分方面的丢番图近似
DOI：
10.3836/tjm/1249648415
复制
发表时间：
2009
影响因子：
0.6
通讯作者：
T. Komatsu
中科院分区：
文献类型：
--
作者：
T. Komatsu
． 设p n /q n为实数α的连分式展开式的n次收敛。我们知道，当n趋于无穷时，| p n−q n α |趋于0是非常小的。本文建立了当α为e型实数且其连分式展开式为拟周期时，如何用积分表示pn−qn α的方法。
. Let p n /q n be the n -th convergent of the continued fraction expansion of a real number α . It is known that | p n − q n α | is very small tending to 0 as n tends to infinity. In this paper we establish a method how to express p n − q n α in terms of integrals when α is an e -type real number and its continued fraction expansion is quasi-periodic.