Thiele rational interpolation for the numerical computation of the reversible Randles-Sevcik function in electrochemistry

This paper uses Thiele rational interpolation to derive a simple method for computing the Randles–Sevcik function π1/2χ(x), with relative error at most 1.9 × 10−5 for −∞ < x < ∞. We develop a piecewise approximation method for the numerical computation of π1/2χ(x) on the union (−∞, −10) ∪ [−10, 10] ∪ (10, ∞). This approximation is particularly convenient to employ in electrochemical applications where four significant digits of accuracy are usually sufficient. Although this paper is primarily concerned with the approximation of the Randles–Sevcik function, some examples are included that illustrate how Thiele rational interpolation can be employed to generate useful approximations to other functions of interest in scientific work.