An Algorithm for the Computation of the Higher Order G-Transformation

The higher order G-transformation as defined in [1] has proved to be a useful transformation for the evaluation of improper integrals of the first kind. This transformation is defined as the ratio of determinants whose order increases as the order of the transformation; consequently, the transformation becomes increasingly more difficult to use as the order increases. This paper introduces an algorithm for the evaluation of the higher order G-transformation that does not require the use of determinants. A connection is also made between the G-transformation and P. Wynn’s continued fraction integral [3].