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Using the theory of spherical symmetric random vectors one can find an expression for the error probability of a wide variety of digital communications systems. These expressions, however, are in the form of Bessel integrals which are usually difficult to solve. In this paper we show how the Fourier-Bessel series can be used to solve the integrals numerically. The calculation error is found to depend on two series parameters which can be manipulated to make the error arbitrarily small. Two examples are used to show the utility of the technique. In the first the probability of error for a CPSK communications system operating in Gaussian noise and cochannel interference is found. In the second the error performance for a multilevel ASK communications system operating in the same corrupting environment is determined. The Fourier-Bessel series technique is a valuable practical tool for solving these and other signal detection problems.