Power law approximations for radioactive decay chains

Consider a radioactive decay chain X1→⋯→Xn→X1→⋯→Xn→ and let Nn(t)Nn(t) be the amount of XnXn at time t  . This paper establishes error bounds for small and intermediate time approximations to Nn(t)Nn(t) including the power-law approximation Nn(t)≈Ctm-1Nn(t)≈Ctm-1 for τm+1<