The Pade rational function in general use as an approximation for the p(X) function or the Arrhenius integral seems to be in error. A corrected equation is given. Even the correct rational function, and other suggested approximating equations, are not accurate enough at low values of X = E/RT. Chebyshev polynomials offer a better solution, over the whole range of X values, to a greater precision than found in published tables. Relatively simple computer routines may be used to generate the coefficients required. The Stander and van Vuuren/Zsako method of analysis of non-isothermal data may be used to test the time of a typical calculation.