$$ \hat{h}^k(s) = \big[1-\theta-\theta\tanh(a\sqrt s)\coth(b\sqrt s)\big]^k\hat{h}^0(s) $$ is true for $k=1,2, \ldots$ and $a>b$, where $s$ is Laplace variable and the relation is after taking Laplace transform and $0<\theta<1$. Now how I show $h^k(t)$ converges?
Thanks in advance.