基于连分式的S_n=∑nk=11/(n^2+k)渐近逼近

Continued Fraction Approximation Related to S_n=∑nk=11/(n^2+k)

针对文献[1]中提出的在一定误差范围内,如何获得数列S_n=∑nk=11/(n^2+k)的渐近公式进行了研究。采用多重校验法得到了该数列的有理函数逼近公式,并且给出了绝对误差界。该方法具有一定的理论和实际应用价值。

Abstract： The aim of this work is to solve the problem in Concrete Mathematics： A Foundation for Computer Science, 2nd edition, P. 458. We obtain some rational approximationsof the sequence Sn=∑nk=11/（n2＋k） by using the multi-correction method. Furthermore, we give some ine-qualities for the upper and lower bounds.