an analytical representation of bivariate isotropic stable density

Stable random vectors are characterized by their characteristic functions. the multivariate stable density and distribution functions generally do not have an analytic form. a few numerical methods have been developed to compute density functions of parametric stable random vectors. however, they have some limitations in terms of the range of the tail index. in this work, via the inversion formula, we present a new analytical representation of the density function of a bivariate isotropic stable random vector. we show that the analytical representation can be reduced to a closed form at the origin.