I am reading about Pfaffian, which can be found here https://en.wikipedia.org/wiki/Pfaffian.
We know that the (general) Laplace expansion is very useful to compute determinants of matrices, and I wonder if there is such an expansion to compute Pfaffians (of skew-symmetric matrices). Fortunately, such formula exists https://en.wikipedia.org/wiki/Pfaffian#Recursive_definition, however I do not know how to prove it.
Do you know any proof or any reference? And what is the general form of such formula, i.e., when we expand along $k>1$ rows and columns?