no. 1
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, C. G. and Van der Poorten, A. 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},
     mrnumber = {1251238},
     zbl = {0789.11002},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1993__5_1_187_0/}
}
TY  - JOUR
AU  - Pinner, C. G.
AU  - Van der Poorten, A. J.
AU  - Saradha, N.
TI  - Some infinite products with interesting continued fraction expansions
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1993
SP  - 187
EP  - 216
VL  - 5
IS  - 1
PB  - Université Bordeaux I
UR  - http://archive.numdam.org/item/JTNB_1993__5_1_187_0/
LA  - en
ID  - JTNB_1993__5_1_187_0
ER  - 
%0 Journal Article
%A Pinner, C. G.
%A Van der Poorten, A. J.
%A Saradha, N.
%T Some infinite products with interesting continued fraction expansions
%J Journal de théorie des nombres de Bordeaux
%D 1993
%P 187-216
%V 5
%N 1
%I Université Bordeaux I
%U http://archive.numdam.org/item/JTNB_1993__5_1_187_0/
%G en
%F JTNB_1993__5_1_187_0
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://archive.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 | Zbl

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