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Some infinite products with interesting continued fraction expansions. (English) Zbl 0789.11002

If the reader wants to learn about infinite products in \(K((x^{-1}))\) of the type \(\prod_ h(1+x^{-\lambda_ h})\) having interesting continued fractions, and to know in particular to what extent the set of truncations and subsets of the set of partial quotients coincide, if he wants to play with transducers in this context, then he should definitely read the paper under review, which contains an enjoyable and rather systematical study of the sequences \((\lambda_ h)\) such that the truncations of the infinite associated product yield (eventually) every \(k\)-th partial quotient.

MSC:

11A55 Continued fractions
68R99 Discrete mathematics in relation to computer science
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References:

[1] Allouche, J.-P., Mendès France, M. and van der Poorten, A.J., An infinite product with bounded partial quotients, Acta Arith.59 (1991), 171-182. · Zbl 0749.11014
[2] Mendès France, M. and van der Poorten, A.J., Some explicit continued fraction expansions, Mathematika, 38 (1991), 1-9. · Zbl 0708.11011
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