Black-hole normal modes: A WKB approach. III. The Reissner-Nordström black hole

Complex frequencies of the normal modes of the Reissner-Nordstr\"om black hole are computed by two independent methods. The first is a high-order WKB approach devised by Schutz and Will and extended by Iyer and Will for the Schwarzschild case. The second is direct numerical integration using a method developed by Chandrasekhar and Detweiler, thereby extending earlier results of Gunter. The WKB results agree with the numerical ones with an error less than 1% for the lowest-order modes. For somewhat higher orders, the numerical techniques fail but the WKB method continues to give eigenfrequencies that should be reasonably accurate.