It sounds like what you are describing are the isentropic compressible flow equations. See equation 6 & 7.
At Mach 2.1, these give a stagnation pressure rise of 9.14, and a stagnation temperature rise of 1.88, since air has a value of 1.4 for gamma.
But, the air does not come to complete rest (stagnation) in the intake, hence these values are not obtained.
What you need to know, is the actual Mach number at the engine inlet, which is I assume where you are suggesting is the location of a total pressure 2.39 times higher than the freestream total pressure. Typically, this is around Mach 0.4. But, since the freestream flow is supersonic, that means it will have had to go through some shock waves, to get to a subsonic speed. This means there will be pressure losses, associated with those shock waves. Normal shock waves (a shock wave perpendicular to the flow) result in higher total pressure losses than oblique shock waves. Hence, supersonic aircraft have pointed cones in their intakes to create oblique shock waves, to minimise the pressure losses. To calculate the total pressure losses from these, you need to know the geometry of these cones to know if they cause 1, 2, or maybe even 3 oblique shock waves, as the pressure loss of each shock depends on the strength of each shock wave.
Jack Mattingly, in his text book "Aircraft Engine Design" gives a good description of how to calculate the losses associated with oblique intake shock waves. It's fairly complex. See here. The figure you want is 10.35, but that wasn't shown in the free preview when I tried it, but maybe the pages they hide are random, and you will have better luck.
So, in summary, to verify the 2.39 factor, you need to know the Mach number at the engine fan inlet, and be able to calculate the total pressure losses of the shock waves, which requires info of the intake geometry.