Pole Approximations in theNDEquations

We propose the use of Padé approximants (which are essentially a prescription for constructing pole approximations) to make the kernels of the $\frac{N}{D}$ integral equations separable. If certain conditions on the function being approximated are satisfied, it can be shown that the sequence of approximate solutions which one obtains will converge to the exact solution. The method is applied to the netural pseudoscalar-pseudoscalar-scalar bootstrap, and the known result is easily reproduced.