Some infinite products with interesting continued fraction expansions
Journal de Théorie des Nombres de Bordeaux, Volume 5 (1993) no. 1, pp. 187-216.

We display several infinite products with interesting continued fraction expansions. Specifically, for various small values of $k$ necessarily excluding $k=3$ since that case cannot occur, we display infinite products in the field of formal power series whose truncations yield their every $k$-th convergent.

DOI: 10.5802/jtnb.89
Classification: 11A55
Keywords: continued fraction, infinite product
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title = {Some infinite products with interesting continued fraction expansions},
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C. G. Pinner; A. J. Van der Poorten; N. Saradha. Some infinite products with interesting continued fraction expansions. Journal de Théorie des Nombres de Bordeaux, Volume 5 (1993) no. 1, pp. 187-216. doi : 10.5802/jtnb.89. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.89/

[1] J.-P. Allouche, M. Mendès France and A.J. Van Der Poorten, An infinite product with bounded partial quotients, Acta Arith. 59 (1991), 171-182. | MR: 1133957 | Zbl: 0749.11014

[2] M. Mendès France and A.J. Van Der Poorten, Some explicit continued fraction expansions, Mathematika, 38 (1991), 1-9. | MR: 1116679 | Zbl: 0708.11011

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