For the derivatives $f^{(k)}_\alpha(x)$ of the one-sided stable density of index $\alpha \in (0, 1)$ asymptotic formulas are computed as $k \rightarrow \infty$ thereby exhibiting the detailed analytic structure for large orders of derivatives. The results extend those for the well-known case $\alpha = \frac{1}{2}$ which may be expressed in terms of Laguerre polynomials (formulas of Plancherel-Rotach type).
@article{1176991695,
author = {Gawronski, Wolfgang},
title = {Asymptotic Forms for the Derivatives of One-Sided Stable Laws},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1348-1364},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991695}
}
Gawronski, Wolfgang. Asymptotic Forms for the Derivatives of One-Sided Stable Laws. Ann. Probab., Tome 16 (1988) no. 4, pp. 1348-1364. http://gdmltest.u-ga.fr/item/1176991695/