Relationship between anomalous factor and alpha

[quiet]

Hello everyone. Maybe you can help me with the following. In the case of the electron, is there any known mathematical relationship between anomalous factor and fine structure constant?

 

[Vanadium 50]

$$a \approx \alpha/2\pi$$ Just like it says in Wikipedia.

 

[quiet]

Thank you ! The wikipedia article exposes the result for a one loop. And for this case indicates that
$$a_e \simeq \dfrac{\alpha}{2 \pi}$$
Let us not think how laborious can be the exact calculation. I am interested only in the concept. Does that mean the following? : there are valid reasons to accept that it really should be
$$a_e = \dfrac{\alpha}{2 \pi}$$

 

[Vanadium 50]

Since it's not exactly α/2π, how could there possibly be valid reasons for it to be exactly α/2π?

 

[quiet]

Thanks Vanadium 50 !