The Hopf Algebroid Structure of Differentially Recursive Sequences

A differentially recursive sequence over a differential field is of elements satisfying homogeneous equation with non-constant coefficients (namely, Taylor expansions the field) in algebra Hurwitz series. The main aim this paper to explore space all sequences given non-zero differential. We show that these form two-sided vector admits, canonical way, structure Hopf algebroid subfield constant elements. prove it direct limit, as left comodule, spaces formal solutions linear equations and satisfies, algebroid, an additional universal property. When on base zero, we recover linearly sequences.