I have a quantum electrodynamics exercise on the one-loop electron self-energy correction in which I need to show that
$$ \tag{1} ie^{2}\Sigma(p)=\frac{\left(-ie\right)^{2}}{\left(2\pi\right)^{4}}\int d^{4}qD_{\lambda\sigma}\left(q\right)\gamma^{\lambda}S_{F}\left(p-q\right)\gamma^{\sigma} $$
where
$$ \tag{2} D_{\lambda\sigma}\left(q\right)=\frac{-i\eta_{\lambda\sigma}}{q^2-i\epsilon} \qquad\qquad S_{F}\left(p\right)=\frac{i\left(\gamma^{\alpha}p_{\alpha}-m\right)}{p^{2}+m^{2}-i\epsilon} $$
can be written as
$$ \tag{3} ie^{2}\Sigma(p)=\frac{e^{2}}{\left(2\pi\right)^{4}}\int d^{4}q\frac{1}{q^2-i\epsilon}\frac{2\left(\gamma^{\alpha}\left(p-q\right)_{\alpha}-2m\right)}{\left(p-q\right)^{2}+m^{2}-i\epsilon} $$
I can get close to show this using $\gamma_{\sigma}\gamma^{\sigma}=4$ and $\gamma_{\mu}\gamma^{\sigma}\gamma^{\mu}=-2\gamma^{\sigma}$, but I wasn't able to do it completely yet. So, the first thing I would like to know is if $D_{\lambda\sigma}\left(q\right)$ and $S_{F}\left(p\right)$ are well defined with this formulas, because the formulas I've studied are different,
$$ D_{\lambda\sigma}\left(q\right)=\frac{-i\eta_{\lambda\sigma}}{q^2+i\epsilon} \qquad\qquad S_{F}\left(p\right)=\frac{i\left(\gamma^{\alpha}p_{\alpha}+m\right)}{p^{2}-m^{2}+i\epsilon} $$
so I want to know if both forms are equivalent. If the first ones are correct, then I cannot show what the exercise asks for. Could you advise?