Integral equations for the spin-weighted spheroidal wave function

Abstract

Integral equations for the spin-weighted spheroidal wave functions is given. For the prolate spheroidal wave function 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. In the paper, we also extend the similar sinc function kernel (sin x)/x to the case m and s both are not zero, which interestingly turn out as some kind of Hankel transformation.

References in corpus (1)

• Asymptotic tails of massive scalar fields in a stationary axisymmetric EMDA black hole geometry

Cited by in corpus (3)

• Study of the Spin-weighted Spheroidal Equation in the Case of s=1
• A new model for the double well potential
• The Spin-weighted Spheroidal Wave functions in the Case of s=1/2