What is an accurate expression to calculate IAS as a function of TAS?
You might look at Ed William's aviation formulary.

http://www.edwilliams.org/avform.htm#Mach

From there:

&gt; The airspeed indicator measures the differential pressure, DP, between
&gt; the pitot tube and the static port, the resulting indicated airspeed
&gt; (IAS), when corrected for calibration and installation error is called
&gt; "calibrated airspeed" (CAS).
&gt; 
&gt; For low-speed (M&lt;0.3) airplanes the true airspeed can be obtained from
&gt; CAS and the density altitude, DA.
&gt; 
&gt;   TAS = CAS*(rho_0/rho)^0.5=CAS/(1-6.8755856*10^-6 * DA)^2.127940
&gt; (DA&lt;36,089.24ft)  Roughly, TAS increases by 1.5% per 1000ft.


Note that you can go from TAS to CAS, but you will need help getting to IAS, specifically the instrument error for that AS indicator in that aircraft.