Convergence of Padé Approximants for the Bethe-Salpeter Amplitude

We extend some earlier work on the Bethe-Salpeter equation to show that the sequence of [$N, N$] Padé approximants to ${tan\delta }_l$ converges to the correct result if the scattered particles are of equal mass. The proof includes a demonstration that the symmetrized kernel of the Bethe-Salpeter equation after a coordinatespace Wick rotation is $L^2$. An interesting connection between Padé approximants and the Schwinger variational principle is given.