  An absolutely convergent double series representation for the density of the
supremum of $\alpha$-stable Levy process is given in [3, Theorem 2] for almost
all irrational $\alpha$. This result cannot be made stronger in the following
sense: the series does not converge absolutely when $\alpha$ belongs to a
certain subset of irrational numbers of Lebesgue measure zero (see [6, Theorem
2]). Our main result in this note shows that for every irrational $\alpha$
there is a way to rearrange the terms of the double series, so that it
converges to the density of the supremum. We show how one can establish this
stronger result by introducing a simple yet non-trivial modification in the
original proof of [3,Theorem 2].
