极限周期连分式sum from n=1 to ∞ 〔a_n/1〕加速收敛的误差估计

Error estimate for accelerating convergence of limit periodic continued fraction sum from n=1 to ∞ 〔a_n/1〕

极限周期连分式是一类非常重要的连分式,它在连分式分析理论中占有极其重要的地位。文章从定量角度出发,对极限周期连分式在一般加速收敛因子下的加速收敛效果进行了研究,并给出了误差表达式。

The limit periodic continued fraction is an important kind of continued fractions,which holds the extremely important status in the continued fraction analysis theory.From a quantitative perspective,this paper conducts the research on accelerating convergence effect of limit periodic continued fraction,and gives the erroneous expression with the general converging factor.