1Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing Aerospace Control Center, Beijing 100094 2Department of Aerospace Guidance Navigation and Control, School of Astronautics, Beihang University, Beijing 100191 3QUEST Center of Quantum Engineering and Space-Time Research, Leibniz Universität Hannover, Hannover 30167, Germany 4Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Hannover 30167, Germany 5Institute of Applied Mathematics, Morningside Center of Mathematics and LESC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190
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 Painlevé transcendent is then worked out explicitly.
2016, Vol. 33 
