| Abstract: | Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background,a homogeneous integral equation related to the prolate spheroidal function is studied.From the consideration of the Fredholm determinant of the integral equation,a family of generalized error function is defined,with which the Fredholm determinant of the sinc kernel is also evaluated.An analytic solution of a special case of the fifth Painleve transcendent is then worked out explicitly. |
