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Refined error estimates for the Riccati equation with applications to the angular Teukolsky equation

We derive refined rigorous error estimates for approximate solutions of 
Sturm-Liouville and Riccati equations with real or complex potentials. The approxi- 
mate 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.