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.


11A55 Continued fractions
11J70 Continued fractions and generalizations
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