Long Series in Mechanics: Janzen–Rayleigh Expansion for a Circle

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Abstract

We reconsider the transonic controversy – whether a given airfoil can exhibit a continuous range of shock-free supersonic flow. We employ the circle as our ‘airfoil’, and examine the Janzen–Rayleigh expansion in even powers of 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.

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