What does the symbol \mathscr{P} in Atom-Photon Interactions stand for?

[Robert_G]

Hi. I am reading a book entitled "Atom-Photon interactions" by Claude Cohen-Tannoudji, et al.
There is a symbol which looks like $\mathscr{P}$. The authors state that this symbol stands for the principle part. e.g.

$\hat{\Delta}_b(E)=\frac{1}{2\pi} \mathscr{P} \int dE' \frac{\hat{\Gamma}_b(E')}{E-E'}$

Principle part usually refers to the negative-power portion of the Laurent series of a function. Now in the above equation, is it true that we need to expand the right hand side of the equation into Laurent series, and only take the negative-power portion from it?

In the context of this book, I have a strong feeling that $\mathscr{P}$ just means $E\neq E'$.

Are you familiar with the definition of the principle part? Please tell me.

 

[UltrafastPED]

Or maybe it is this: http://mathworld.wolfram.com/CauchyPrincipalValue.html