Abstract
An integral of a triple product of associated Legendre functions was analytically evaluated by GAUNT (1929). His formula for the evaluation of the integral can not readily be executed by a fortran computer program because of the mathematical complexity. A convenient method of evaluating the integral by means of recurrence relations of Legendre functions is obtained. The integral thus obtained is applied to the truncation error estimate for the Stokes integration extended over an arbitrarily-shaped area and to the Molodenskii correction for the geoidal-height estimation.
