Forms of Nelson Siegel formula

Question

Are these two forms of Nelson Siegel formula equivalent?

$s_{m}(\beta )=\beta _{0}+\beta _{1}\frac{1-e^{\frac{-m}{\tau _{1}}}}{\frac{m}{\tau _{1}}}+\beta _{2}\left ( \frac{1-e^{\frac{-m}{\tau _{1}}}}{\frac{m}{\tau _{1}}}-e^{\frac{-m}{\tau _{1}}} \right)$

$s_{m'}(\beta )=\beta _{0}+\beta _{1}\frac{1-e^{-m\tau _{1}}}{m\tau _{1}}+\beta _{2}\left ( \frac{1-e^{-m\tau _{1}}}{m{\tau _{1}}}-e^{-m\tau _{1}} \right)$

Answer 1

Those expressions are certainly not equivalent for the same $\tau$ (e.g. consider what happens when $\tau\rightarrow 0^+$). The first kind of formulation is used in the Nelson Siegel 1987 paper. It is possible the second one may be an alternate parametrization.