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Dimensional regularization is a method of isolating divergencies in scattering amplitudes.
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Limit of $d\rightarrow 4$ of a function in Peskin & Schroeder
As other terms are trivial, I will calculate $\displaystyle \lim_{d \to 4}\frac{1-b^{d-4}}{d-4}$ only. Let $x:=d-4$, then lim becomes
$\displaystyle \lim_{x \to 0}\frac{1-b^x}{x-0}=-\frac{db^x}{dx}|_{ …