Calculation and Application of Infinite Ordinary Continued Fractions
ZHOU Tong;ZHONG Zhihua;School of Mathematical Sciences,Fudan University;School of Sciences,Nantong University;
Two methods were proposed for calculating infinite ordinary continued fractions. The infinite continued fraction was converted into a recurrence relation of a sequence. If the sequence is convergent, the value of the infinite continued fraction is the limit of the sequence. For the first method, the limit was obtained by solving a corresponding equation. In the second approach, the Fibonacci sequence was used to write down the explicit expression for a general term of the sequence. Then the value of the infinite continued fraction was obtained by directly taking the limit in the expression. Besides that, the iteration process of evaluating infinite continued fractions can be intuitively shown by drawing diagrams. Moreover, based on the first approach, an iterative algorithm was developed, which can naturally lead to the Picard iteration method in solving ordinary differential equations.
【CateGory Index】： O156