|ISSN 1088-6842(online) ISSN 0025-5718(print)|
Conversion of continued fractions into power series
Abstract: In Section 1, continued fractions of the special form
are considered, and a general formula is given for the coefficients of the power series corresponding to (1). In Section 2, the problems of programming the computation of coefficients are discussed.
The continued fraction (1), or its variants, has been studied by many distinguished mathematicians. The problem of converting (1) into a power series has also been considered, and a number of partial results are known. A detailed account can be found in Perron .
In this paper, we will not make use of the techniques that are generally applied in the theory of continued fractions. Instead, our approach employs some simple combinatorial and probabilistic arguments. Nevertheless, the methods are quite elementary and can be understood even by those who are unfamiliar with probability theory.