Can anything be said about the Fourier integral


$\int\_{-\infty}^{\infty} \exp\left[ika - (\gamma + ik)^{2/3}\right]dk$


where $a > 0$ and $\gamma > 0$?


Can it be related to some special function? It appears in the physics application described [in this MO question](http://mathoverflow.net/questions/22281/can-i-relate-the-l1-norm-of-a-function-to-its-fourier-expansion).



Integral involving exponential of fractional power
upon a change of variables, $\gamma+ik\mapsto ik'$ it takes the form of the generating function of a socalled stable distribution (with stability parameter $\alpha=2/3$
<http://en.wikipedia.org/wiki/Stable_distribution>


