Let F be a rational function of x over a field K of characteristic 0. The PolynomialNormalForm(F,x) command constructs the differential polynomial normal form for F.

The output is a sequence of 3 elements  where  are polynomials over K such that:

 for all non-negative integers .

.

Almkvist, G, and Zeilberger, D. "The method of differentiating under the integral sign." Journal of Symbolic Computation. Vol. 10. (1990): 571-591.