Generalized Separants of Differential Polynomials / M. A. Limonov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 6. P. 9-14
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 248-252].
Let f\in K\{y\} be an element of the ring of differential polynomials in one differential
variable y with one differential operator \delta .
For any variable y_k, the polynomial g=\delta^n(f) can be represented in the form g=A_ky_k+g_0,
where g_0 does not depend on y_k. If y_k is the leader of g, then A_k is a separant
of the polynomial f. A formula for A_k is obtained for sufficiently large numbers n and k
and some applications of this formula are presented.