Generator of QED in path integral approach

Consider the interacting field Lagrangian density of the real KG field
begin{equation}mathscr{L}=frac{1}{2}partial_muphipartial^muphi-frac{m^2}{2}phi^2-frac{lambda}{4!}phi^4
end{equation}
The generating functional for the theory is
begin{equation}
W[J]=intmathscr{D}phi(x)expleft(iint d^4xleft[frac{1}{2}partial_muphipartial^muphi-frac{m^2}{2}phi^2-frac{lambda}{4!}phi^4+Jphi right]right)
end{equation}
the surface terms vanishes at infinity gives
$$begin{align}
W[J]=intmathscr{D}phi(x)expleft(-iint d^4xleft[frac{1}{2}phi(partial^2+m^2)phi+frac{lambda}{4!}phi^4-Jphi right]right)nonumberhspace{5cm}=expleft(iint d^4xmathscr{L}_I(-ifrac{delta}{delta J(x)})right)W_0[J]
hspace{8cm}nonumber=expleft(iint d^4xmathscr{L}_I(-ifrac{delta}{delta J(x)})right)expleft(frac{-i}{2}int J(x)Delta_F(x-y)J(y)d^4xd^4yright)intmathscr{D}phi(x)exp(i S_{free}) label{p24}
end{align} $$

For QED
The Lagrangian density is
$$mathscr{L}=overlinepsi(igamma^mumathcal{D}_mu-m)psi-frac{1}{4}F_{munu}F^{munu}=overlinepsi(igamma^mupartial_mu-m)psi-frac{1}{4}F_{munu}F^{munu}-tilde{e}overline{psi}gamma^mu A_mupsi$$
and the corresponding generating functional
is
begin{equation}
W[eta,bar{eta},eta_mu]=intmathscr{D}psi(x)mathscr{D}overline{psi}(x)mathscr{D}A_mu(x)expleft(iint d^4x(mathscr{L}+ overline{psi}eta+overline{eta}psi+eta_mu A^mu)right)
end{equation}

$$W[eta,bar{eta},eta_mu]= expBigg(-itilde{e}int d^4x left(-frac{1}{i}frac{delta}{deltaeta}right)gamma^muleft(-frac{1}{i}frac{delta}{deltaeta^mu}right)left(-frac{1}{i}frac{delta}{deltabar{eta}}right) Bigg)W_0[eta,bar{eta},eta_mu]
$$I argued this by in anolagy with $lambdaphi^4$ theory.I search several books like Ryder,Peskin and Shroeder,Zee and Stefen pokorski for getting an explicit form for $W[eta,bar{eta},eta_mu]$ and $W_0[eta,bar{eta},eta_mu]$,But I didn’t get it…

My question is what is the explicit form of $W_0[eta,bar{eta},eta_mu]$ for QED?