We investigate the continued fraction expansion of the infinite products
g(x)=xβ1βt=0ββP(xβdt) where polynomials P(x) satisfy
P(0)=1 and deg(P)<d. We construct relations between partial quotients of
g(x) which can be used to get recurrent formulae for them. We provide that
formulae for the cases d=2 and d=3. As an application, we prove that for
P(x)=1+ux where u is an arbitrary rational number except 0 and 1, and for
any integer b with β£bβ£>1 such that g(b)ξ =0 the irrationality exponent
of g(b) equals two. In the case d=3 we provide a partial analogue of the
last result with several collections of polynomials P(x) giving the
irrationality exponent of g(b) strictly bigger than two.Comment: 25 page