Exact expressions for the moments of ladder heights

With the aid of the formula for the Laplace transform of a contraction of a distribution on the positive semiaxis the formulas for moments of the ascending ladder height are deduced for each of the three cases: the null, positive and negative expectation of a step in the random walk. The results are formulated in terms of the moments and integral functionals of the characteristic function of the step function. Despite the complexity of the proof the final formulas are comparatively simple.