Talk:Pincherle derivative

"ad"?

This article begins with this definition:

the Pincherle derivative of a linear operator

\scriptstyle {T:\mathbb {K} [x]\longrightarrow \mathbb {K} [x]}

on the vector space of polynomials in the variable

\scriptstyle x

over a field

\scriptstyle {\mathbb {K} }

is another linear operator

\scriptstyle {T':\mathbb {K} [x]\longrightarrow \mathbb {K} [x]}

defined as

T'=[T,x]=Tx-xT=-\operatorname {ad} (x)T,\,

so that

T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad \forall p(x)\in \mathbb {K} [x].