Derivative-free inversion of Abel’s integral equation

We present a new inversion formula for Abel’s integral equation which does not require derivatives of any of the functions involved. This is a particularly desirable feature when analyzing experimentally derived data, since differentiation enormously amplifies the random errors inherent in all measured data. The high quality of the results obtainable using the new formula is demonstrated by a typical numerical example for which it yields errors smaller by an order of magnitude than those obtained with the usual inversion formula.