Integral Equations for the Spin-Weighted Spheroidal Wave unctions

We present new integral equations for the spin-weighted spheroidal wave fuctions which in turn should lead to global uniform estimates and should help in particular in the study of their dependence on the parameters. For the prolate spheroidal wavefunction with m=0, there exists the integral equation whose kernel is (sin x)/x, and the sinc function kernel (sin x)/x is of great mathematical significance. We also extend the similar sinc function kernel (sin x)/x to the case m≠0 and s≠0, which interestingly turn out as some kind of Hankel transformations.