A few days ago (see this), I asked a question regarding the derivatives of the function $$P_2(x,t)=\frac{\sqrt{2}e^{-t/4}}{(4\pi t)^{3/2}}\int_x^\infty\frac{se^{-s^2/4t}ds}{\sqrt{\cosh(s)-\cosh(x)}}.$$
I was trying to check that $P_2$ satisfies the equation $$\frac{\partial^2 P_2}{\partial x^2}+\coth(x)\frac{\partial P_2}{\partial x}-\frac{\partial P_2}{\partial t}=0,$$ as asked in ''Eigenvalues in Riemannian Geometry'' by Isaac Chavel (pp. 242-246): However, calculations are too heavy for Mathematica to compute them and when derivating by hand over the formulas given in answers to the previous question, I fail to get zero. Is there something else I could try to verify that $P_2$ is in fact a fundamental solution?