I'm new at these things. How will I use the generator
$B_n(z)=\frac{D}{e^D-1}z^n$ where $D= \frac{d}{dz}$ is differentiation with respect to $z$ and the fraction is expanded as a formal power series.
How will I let the operator $D$ act on $z^n$? D is defined as d/dz. I have the idea of expanding $exp$ as a power series and applying $z^n$ to both the numerator and denominator.
Sorry for asking a stupid question. I am not a math major and my math background is only on complex analysis, ODEs, linear algebra, and calculus.
Expand $\frac{D}{e^D-1}$ as a formal series around the origin as
$$\frac{D}{e^D-1} = \sum_{k=0}^\infty a_n D^n.$$
Then apply this formal operator to $z^n$. You get a polynomial as only a finite number of derivatives are not vanishing.