The integration is preformed using the QAWF method in the GSL library for C. For this distribution the Rosinski measure R(dx) = c*delta_ell(dx) + c*delta_(-ell)(dx), where delta is the delta function. The Levy measure is M(dx) = c*ell^(alpha) *e^(-x/ell)*x^(-1-alpha) dx. The characteristic function is, for alpha not equal 0,1:
f(t) = exp( 2*c*gamma(-alpha)*(1+ell^2 t^2)^(alpha/2)*(cos(alpha*atan(ell*t))-1)) *e^(i*t*mu),
for alpha = 1 it is
f(t) = (1+ell^2 t^2)^c*exp(-2*c*ell*t*atan(ell*t)) *e^(i*t*mu),
and for alpha=0 it is
f(t) = (1+t^2 ell^2)^(-c) *e^(i*t*mu).