Some details about function "buttord"

As we all know, function "buttord" is used to returns the order N and the "3 dB frequency" of the lowest digital Butterworth filter. In the function prototype, at first, prewarp frequencies from digital (unit circle) to analog. In this part, there is:

if strcmp(opt,'z')  % digital
  WP=tan(pi*wp/2);
  WS=tan(pi*ws/2);

However, I remember that word in my book. "Usually,In order to make the frequency of analog filter has one-to-one correspondence with any frequency of digital filter, we need to improt a constant c. which is:

     Ω=c*tan(Ω1*T/2);

So, in the function "buttord", c is used in the value of 1. That confuses me so much. How could this happen or what does the writer mean?