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Conversion of continued fractions into power series

Authors: A. J. Zajta and W. Pandikow
Journal: Math. Comp. 29 (1975), 566-572
MSC: Primary 40A15; Secondary 60J15
MathSciNet review: 0412655
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Abstract: In Section 1, continued fractions of the special form

$\displaystyle [unk]$ ($ 1$)

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 [1].

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.

References [Enhancements On Off] (What's this?)

  • [1] O. PERRON, Die Lehre von den Kettenbrüchen, Chapter 8, München, 1929; Reprint, Chelsea, New York.

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Keywords: Continued fractions, power series, conversion formula, partitions, random variables, random walk with a barrier, generating functions, convolution formula, algorithm for generating partitions, pointer addresses, memory space, memory locations
Article copyright: © Copyright 1975 American Mathematical Society

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