thermal, with a high-energy tail that may be characterized by a power law. This led @band93 to propose an entirely phenomenological spectral form that is the unique function joining two power laws that is continuous and smooth to first order: the ‘Band’ GRB function. This function finds its most familiar form in equation \[bandmodel\], in a parametrization where the break energy is cast as the peak in the spectral energy distribution ($E^2 f_{\rm Band}(E)$ or $\nu {\cal F}_{\nu}$): [$E_{\rm peak}$]{}. $$\begin{aligned}
f_{\rm Band}(E) & = & A \left( \frac{E}{100 \; {\rm keV}}\right)^{\alpha} 
\exp \left(-\frac{E\; (2+\alpha)}{E_{\rm peak}}\right)\nonumber\\
{\rm if} \quad E & < & \frac{(\alpha-\beta)\; E_{\rm peak}}{(2+\alpha)} 
\equiv E_{\rm break} {\rm ,}\nonumber\\
\quad f_{\rm Band}(E) & = & A \left[\frac{(\alpha-\beta) \; E_{\rm peak}}
{(2+\alpha)\; 100\; {\rm keV}}\right]^{(\alpha-\beta)}\label{epmod} \times \nonumber\\
&  & \exp{(\beta-\alpha)} \left(\frac{E}{100 \; {\rm keV}}\right)^{\beta}\nonumber\\
{\rm if} \quad E & \geq & \frac{(\alpha-\beta)\; E_{\rm peak}}{(2+\alpha)}{\rm .} \label{bandmodel}\end{aligned}$$ From the form of the function, both $\alpha$ and $\beta$ are power law indices in photon number. Because of the pre-factor $E^2$ in the definition of $\nu {\cal F}_{\nu}$, [$E_{\rm peak}$]{} is only defined for values of $\beta$ less than $-2$ (as is typical). For large negative values of $\beta$, we recover thermal-like 