Extension of perturbation series by computer - Symmetric subsonic potential flow past a circle

Seven terms in an expansion for small Mach number (the Janzen-Rayleigh approximation) for the compressible inviscid flow about a circular cylinder without circulation are determined by computer. The critical Mach number for gamma equals 7/5 is found to be about 0.3983. Convergence of the series for maximum surface speed is investigated using the graphical method of Domb and Sykes. As expected, the solution is singular on the positive real axis of M squared. Seven terms in the series are sufficient only to determine that the radius of convergence lies somewhere within a 5.5 percent spread of the critical Mach number.