Inhomogeneous differential approximants for power series

Abstract

Inhomogeneous differential approximants (J/L;M)f(x), (J/L;M,N)f(x,y) etc. are defined for functions of one or more variables given as power series expansions, and some of their properties are exposed. The approximants are easily computable, and numerical studies are reported (for single-variable series) which demonstrate their utility in circumstances where the customary direct or logarithmic derivative Pade approximants (which are limiting cases) are inadequate.