On the method of Chan and Lu for Abel's integral equation

For the method proposed recently by Chan and Lu (1981) for the inversion of Abel's integral equation, the authors show that (i) under a wide range of circumstances, it yields numerical schemes identical with those obtained from the direct discretisation of the standard inversion formulae; (ii) although it avoids the explicit numerical differentiation in the standard inversion formulae, it does not avoid the numerical difficulties inherent in the inversion; and (iii) it is still equivalent mathematically and numerically to a half-differentiation.