I am reading a paper about one sided stopping rule. On the 2nd page and line 16-17, the author has that $\lambda=(c/\mu)^{1/(1-\alpha)}$ and the author lets $x$ be arbitrary and assume that $n$ is a function of $c$ such that $$[cn^\alpha-n\mu](\sigma n^{\frac{1}{2}})^{-1}=-x,\tag{1}$$ then the author says that so by inversion, we have $$[n-\lambda][(1-\alpha)^{-1}\lambda^{0.5}\mu^{-1}\sigma]^{-1}\rightarrow x.\tag{2}$$
My question is that how does the author derives the (2) equation using (1) ? Can anyone share some insights and what is the meaning of $\rightarrow$ which the author did not define this symbol before? Thank you (It should be easy but I am confused here)
After a lot energy on proving this, I find out that there is a lot of details left over to reader in this paper. Later on I find another paper by Allan Gut who explains this issue clearly. For details see "On the moments and limit distributions of some first passage times" By Allan Gut.