Pincherle derivative

In mathematics, the Pincherle derivative^[1] ${\displaystyle T'}$ of a linear operator ${\displaystyle T:\mathbb {K} [x]\to \mathbb {K} [x]}$ on the vector space of polynomials in the variable x over a field ${\displaystyle \mathbb {K} }$ is the commutator of ${\displaystyle T}$ with the multiplication by x in the algebra of endomorphisms ${\displaystyle \operatorname {End} (\mathbb {K} [x])}$. That is, ${\displaystyle T'}$ is another linear operator ${\displaystyle T':\mathbb {K} [x]\to \mathbb {K} [x]}$