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General formulas for the accurate computing of the field strength near the reflection point of an electromagnetic wave impinging vertically upon a horizontally stratified ionosphere are derived by means of a uniform approximation valid throughout the whole reflection region. Smoothly varying profiles of general shape but with the gross features determined by the presence of one or two transition points are assumed. Coupling and nonlinear effects are not explicitly included. Since the uniform approximation method is analytic in its essence, it is in many respects more versatile than existing brute force numerical methods.