Numerical conversion between the Pearson VII and pseudo-Voigt functions

The shape coefficient of a curve, which is defined as the ratio of its full width at half-maximum intensity to integral width, is a measure of variation in shape. From the definitions of the pseudo-Voigt, Pearson VII and Voigt functions used in X-ray diffractometry, three shape-converting formulae are deduced. Numerical solution helps to establish a numerical model for interconverting the shapes of the pseudo-Voigt, Pearson VII and Voigt functions. Assessment of the error level and some comments on the shape of the pseudo-Voigt and Pearson VII functions are thereby made.