1-loop Vacuum energy of a fermion field

Following the method by Peskin and Shroesder 11.4 Trying to calculate the vacuum energy of a fermion. If my method is correct so far the next step is to find gamma function , the formula I have for gamma fuctions doesn’t match this equation. Can anyone help with the next step?
Start with the Lagrangian
$$
L=i bar{Psi} partial / Psi-m_{e} bar{Psi} Psi-lambda Psi bar{Psi} phi$$

Epanding about the classical field $$Psi_{c l}+zeta quad bar{Psi}=bar{Psi}_{c l}+bar{zeta} quad phi rightarrow phi_{c l}+rho$$

$$L=ileft(bar{Psi}_{c l}+bar{zeta}right) partialleft(Psi_{c l}+zetaright)-m_{e}left(bar{Psi}_{c l}+bar{zeta}right)left(Psi_{c l}+zetaright)$$
$$-lambdaleft(bar{Psi}_{c l}+bar{zeta}right)left(Psi_{c l}+zetaright)left(phi_{c l}+rhoright)$$
The only terms quadratic with with $zetabar{zeta}$ are $$bar{zeta}i gamma^{mu} partial_{mu} zeta-m_{e} bar{zeta} zeta-lambda bar{zeta} zetaleft(phi_{c l}+rhoright)$$
therefore $$left[-frac{delta^{2} L_{1}}{deltabar{Psi}(x) deltaPsi(y)}right]=i gamma^{mu} partial_{mu}-m_{e}-lambdaleft(phi_{c l}+rhoright)=i gamma^{mu} partial_{mu}-M_{e}$$
This is the Dirac wave operator with $$M=m_{e}+lambdaleft(phi_{c l}+rhoright)$$

Following the same procedure in the book we put this into the effective action and we then need to calculate $$operatorname{Tr} log left(gamma^{mu} partial_{mu}+mright)=sum_{p} log left(gamma^{mu} p_{mu}+mright)$$
$$=V T int frac{d^{4} p}{(2 pi)^{4}} log left(gamma^{mu} p_{mu}+mright)=V T frac{partial}{partial a} int frac{d^{4} p}{(2 pi)^{4}} frac{1}{left(gamma^{mu} p_{mu}+mright)^{a}}|_{a=0}$$

Here I am stuck, as my gamma function formula doesn’t match