Ever need to convert between specular exponent, roughness, and glossiness? for the Blinn-Phong BRDF, these three values represent the same concept. Specular Exponent is the actual value used to compute the BRDF. Let’s call that variable 
$$g = 1 – m \, ,$$
$$m = 1 – g \, .$$
The exponent is given by
$$e = \frac{2}{m^2} – 2$$
or
$$e = \frac{2}{{(1 – g)}^2} – 2 \, .$$
The BRDF 
$$ f_r(\omega_i, \omega_o) = \pi \frac{F(\omega_i \cdot \omega_h) D(\omega_i) G_2(\omega_i \cdot \omega_g, \omega_o \cdot \omega_g)}{4 (\omega_i \cdot \omega_g) (\omega_o \cdot \omega_g)}$$
where Blinn-Phong 
$$ D_{\mathrm{Blinn-Phong}}(\omega_i, \omega_h, e) = \frac{e+2}{2\pi} (\omega_i \cdot \omega_h)^e $$
and the resulting specular illumination is given by
$$ \mathbf{L}_o = f_r(\omega_i, \omega_o) \mathbf{L}_i (\omega_i) \mathbf{V}_i (\omega_i) (\omega_g \cdot \omega_i) \, . $$
