## An infinite product with bounded partial quotients.(English)Zbl 0749.11014

The authors consider the partial quotients of the continued fraction expansions for the infinite products $$\prod^ \infty_{h=0}(1+X^{- k^ h})$$ viewed as Laurent series in $$X^{-1}$$ over a ground field $$K$$. Then they show that when $$k=3$$ and $$K$$ has characteristic zero or 3 then each of the partial quotients is a polynomial in $$X$$ of degree 1. For $$k>3$$ and odd they show that two of any 3 partial quotients are of degree 1. The case of even $$k$$ has been considered by two of the authors elsewhere.

### MSC:

 11A55 Continued fractions 11J70 Continued fractions and generalizations
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