  A multi-peaked version of the analytically extended function (AEF) intended
for approximation of multi-peaked lightning current wave-forms will be
presented along with some of its basic properties. A general framework for
estimating the parameters of the AEF using the Marquardt least-squares method
(MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a
given charge trans-fer and specific energy will also be described. This
framework is used to find parameters for some common single-peak wave-forms and
some advantages and disadvantages of the approach will be discussed.
