Talk:Pincherle derivative

"ad"?
This article begins with this definition: It doesn't say what "ad" is. It should. Michael Hardy (talk) 23:51, 3 July 2009 (UTC)
 * 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
 * $$ T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad\forall p(x)\in \mathbb{K}[x].$$
 * so that
 * $$ T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad\forall p(x)\in \mathbb{K}[x].$$
 * $$ T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad\forall p(x)\in \mathbb{K}[x].$$
 * $$ T'\{p(x)\}=T\{xp(x)\}-xT\{p(x)\}\qquad\forall p(x)\in \mathbb{K}[x].$$