I'm studying the infinite grid resistor problem, and I've noticed that at some point Mathematica solution diverges with the one that's on the theorical study
$$\frac{1}{i\pi}\int_{0}^{\pi}\frac{1-e^{i \arccos(2-\cos(\alpha))}\cos(\alpha)}{\sin( \arccos(2-\cos(\alpha)))}d\alpha$$
The problem is that the site gives following answer:
$$\frac{2}{\pi}$$
While Mathematica gives this to me:
$$-\frac{2}{\pi}$$
The sign is the opposite. So I'd like to know what's I didn't understood.
This is the command that I've used for making the integral:
R11 = 1/(Pi I) Integrate[(1 - Exp[I (ArcCos[2 - Cos[a]])] Cos[a])/Sin[ArcCos[2 - Cos[a]]], {a, 0, Pi}]
I'd like to know what I'm doing wrong and how can I fix it.
NIntegrate
gives the same answer asIntegrate
to several significant figures. $\endgroup$