I have a set of $N$ numbers $\lbrace \lambda_i\rbrace_{i\in[1,N]}$ that belong to $[0,2\pi[$ and a real number $L$ and I am trying to evaluate the following Pfaffian expression.
$$\mathrm{Pf}\left(\frac{\frac{\lambda_j }{i \tan(\frac{\lambda_j L}{2})}-\frac{\lambda_i }{i \tan(\frac{\lambda_i L}{2}) }}{ (\lambda_i+\lambda_j)} \right)$$
The tangent functions are well defined so there is no problem with that.
I know that there exists a similar Pfaffian which is called the Schur Pfaffian which is exactly computed $$\mathrm{Pf}\left(\frac{\lambda_j-\lambda_i }{ \lambda_i+\lambda_j} \right)=\prod_{i<j}\frac{\lambda_j-\lambda_i}{\lambda_j+\lambda_i} $$
