Let $q$ be the density function of the absolute value of a strictly stable random vector in $R^N, N$-dimensional Euclidean space. Asymptotic expressions for $q(r)$ for large $r$ and for small $r$ are found. The proofs use the Fourier inversion formula and contour integration. Bessel functions play a role occupied by the exponential and trigonometric functions when $N = 1$.
Bert Fristedt. "Expansions for the Density of the Absolute Value of a Strictly Stable Vector." Ann. Math. Statist. 43 (2) 669 - 672, April, 1972. https://doi.org/10.1214/aoms/1177692651