 Symmetric stable distribution

A symmetric stable distribution has this characteristic function, with $c>0$ and location $\mu$. At location zero it is a strictly stable distribution: weighted sums of independent copies have scale factor $({\sum }_j|a_j{|}^{\alpha }{)}^{1/\alpha }$. The index $\alpha$ need not permit a finite mean or variance. The scale in this convention is $c^{1/\alpha }$, so the coefficient of $|t{|}^{\alpha }$ and the scale parameter should not be confused.