On the boundary of an immediate attracting basin of a hyperbolic entire function

Let f be a transcendental entire function of finite order which has an attracting periodic point z₀ of period at least 2. Suppose that the set of singularities of the inverse of f is finite and contained in the component U of the Fatou set that contains z₀. Under an additional hypothesis we show that the intersection of U with the escaping set of f has Hausdorff dimension 1. The additional hypothesis is satisfied for example if f has the form f (z) =₀ᶻ p (t) e^q (t) dt+c with polynomials p and q and a constant c. This generalizes a result of Bara\'nski, Karpi\'nska and Zdunik dealing with the case f (z) = eᶻ.