Long series in mechanics: Janzen-Rayleigh expansion for a circle

We reconsider the transonic controversy - whether a given airfoil can exhib it a continuous range of shock-free supersonic flow. We employ the circle a s our 'airfoil', and examine the Janzen-Rayleigh expansion in even powers o f the free-stream Mach number, which we previously carried to 29 terms. In addition to expressing doubt about our previous conclusions, we introduce a promising modification of the graphical ratio test of Domb and Sykes.