  Using the quantum statistical method, the difficulty of solving the wave
equation on the background of the black hole is avoided.We directly solve the
partition functions of Bose and Fermi field on the background of an
axisymmetric Kerr-Newman black hole using the new equation of state density
motivated by the generalized uncertainty principle in the quantum gravity. Then
near the black hole horizon, we calculate entropies of Bose and Fermi field
between the black hole horizon surface and the hypersurface with the same
inherent radiation temperature measured by an observer at an infinite distance.
In our results there are not cutoffs and little mass approximation introduced
in the conventional brick-wall method. The series expansion of the black hole
entropy is obtained. And this series is convergent. It provides a way for
studying the quantum statistical entropy of a black hole in a non-spherical
symmetric spacetime.
