Methods and Applications of Analysis
Volume 22 (2015)
Refined error estimates for the Riccati equation with applications to the angular Teukolsky equation
Pages: 67 – 100
We derive refined rigorous error estimates for approximate solutions of Sturm-Liouville and Riccati equations with real or complex potentials. The approximate solutions include WKB approximations, Airy and parabolic cylinder functions, and certain Bessel functions. Our estimates are applied to solutions of the angular Teukolsky equation with a complex aspherical parameter in a rotating black hole Kerr geometry.
error estimates, Riccati equation, Sturm-Liouville equations, angular Teukolsky equation
2010 Mathematics Subject Classification
34A30, 34A45, 34E20