Some infinite products with interesting continued fraction expansions
Journal de Théorie des Nombres de Bordeaux, Tome 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.

Classification : 11A55
Mots clés : continued fraction, infinite product
@article{JTNB_1993__5_1_187_0,
author = {Pinner, Christopher G. and van der Poorten, Alferd J. and Saradha, N.},
title = {Some infinite products with interesting continued fraction expansions},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {187--216},
publisher = {Universit\'e Bordeaux I},
volume = {5},
number = {1},
year = {1993},
zbl = {0789.11002},
mrnumber = {1251238},
language = {en},
url = {http://www.numdam.org/item/JTNB_1993__5_1_187_0/}
}
TY  - JOUR
AU  - Pinner, Christopher G.
AU  - van der Poorten, Alferd J.
TI  - Some infinite products with interesting continued fraction expansions
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 1993
DA  - 1993///
SP  - 187
EP  - 216
VL  - 5
IS  - 1
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_1993__5_1_187_0/
UR  - https://zbmath.org/?q=an%3A0789.11002
UR  - https://www.ams.org/mathscinet-getitem?mr=1251238
LA  - en
ID  - JTNB_1993__5_1_187_0
ER  - 
Pinner, C. G.; Van der Poorten, A. J.; Saradha, N. Some infinite products with interesting continued fraction expansions. Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 187-216. http://www.numdam.org/item/JTNB_1993__5_1_187_0/

[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