The computation of ELF radio wave fields in the Earth-ionosphere duct

Evaluation of ELF radio wave fields using the mode theory requires the computation of Legendre functions. Four different representations of the Legendre functions in terms of hypergeometric series have been programmed for computation on a microcomputer. By an appropriate choice of series for given values of the propagation constant and distance from the source, only a few (typically eight) terms are needed to calculate the Legendre functions with a precision of six decimal digits.