  The continued fraction method (also known as Leaver's method) is one of the
most effective techniques used to determine the quasinormal modes of a black
hole. For extremal black holes, however, the method does not work (since, in
such a case, the event horizon is an irregular singular point of the associated
wave equation). Fortunately, there exists a modified version of the method,
devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for
neutral massless fields around an extremal Reissner-Nordstrom black hole. In
this paper, we generalize the ideas of Onozawa et al. to charged massless
perturbations around an extremal Reissner-Nordstrom black hole and to neutral
massless perturbations around an extremal Kerr black hole. Similarities and
differences between the results of the original continued fraction method for
near extremal black holes and the results of the new continued fraction method
for extremal black holes are discussed.
