Asymptotic behaviors of Hausdorff dimensions of radial Julia sets of exponential and cosine functions

In this paper, we obtained a four terms asymptotic formula of the Hausdorff dimension of the radial Julia set Jr(fλ) for the exponential function fλ(z) = λez as λ → 0. Moreover, we also discussed the asymptotic behavior of the Hausdorff dimension of the radial Julia set of cosine functions fa,b(z) = aez + be−z as a, b → 0 in various ways.