Sequential radioactive decay
= Sequential radioactive decay
In a chain $N_1\to N_2\to N_3$ with distinct decay constants, the <Bateman equation> expresses each population as a <linear combination> of the <exponential functions> $e^{-\lambda_i t}$. When two consecutive constants coalesce to $\lambda$, the repeated <Laplace transform> pole produces a term proportional to $t e^{-\lambda t}$.