Expression for Ripple factor in Inverse Chebyshev

[MrOmnos]

When normalizing a inverse Chebyshev is it the Pass band cutoff frequency w_p set to 1rad/s or is it stop band w_s frequency set to 1 rad/s?
I derived the following expression for the ripple factor E by normalizing w_p = 1.



But the expression different in text book. It seems they have set w_s frequency set to 1 rad/s and used expression for minimum attenuation at stop band to derive the equation. Hence, they have a different expression where they have alpha_min in their expression. What am I missing here? Why did they do that?

[MrOmnos]

Ahh I get now!!