THE D(2)-TRANSFORMATION FOR INFINITE DOUBLE SERIES AND THE D-2-TRANSFORMATION FOR INFINITE DOUBLE INTEGRALS

New transformations for accelerating the-convergence of infinite doubl e series and infinite double integrals are presented. These transforma tions are generalizations of the univariate d- and D-transformations. The D-2-transformation for infinite double integrals is efficient if t he integrand satisfies a p.d.e. of a certain type. Similarly, the d(2) -transformation for double series works well for series whose terms sa tisfy adifference equation of a certain type. In both cases, the appli cation of the transformation does not require an explicit knowledge of the differential or the difference equation. Asymptotic expansions fo r the remainders in the infinite double integrals and series are deriv ed, and nonlinear transformations based upon these expansions are pres ented. Finally, numerical examples which demonstrate the efficiency of these transformations are given.