Generalized separants of differential polynomials

M. A. Limonov

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 9-14

Résumé

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.