Convergence-accelerating methods have been applied to series expansions for the stable-law density Q(alpha)(z) = 1/pi integral-infinity/0 e(-ualpha) cos(zu) du which is, in turn, simply related to the spectral density of the Kohlrausch-Williams/Watts (KWW) decay function phi(t)=e-(t/tau)alpha]. N.m.r. relaxation parameters such as NOEF, T1 and T1rho are computed for polycarbonate and polydimethylsiloxane using the new series and the results compared to experiment and to earlier computations which employed a decomposition of the KWW function into a sum of exponential terms.