Time-dependent correlation and the evaluation of the stretched exponential or Kohlrausch–Williams–Watts function

An elementary discussion of time-dependent correlation functions is presented. These functions are discussed in the context of dielectric relaxation and nuclear magnetic resonance for two forms of decay: Simple exponential and stretched (Kohlrausch–Williams–Watts) exponential. A guide to the calculation of the stretched exponential fitting parameters using numerical methods is given. Computational notes include comments on the truncation of mathematical series used.