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The dispersion equation for parallel whistler-mode propagation in a hot anisotropic plasma is analysed numerically in both weakly relativistic and nonrelativistic approximations under the assumption that wave growth or damping does not influence the wave refractive index. The results of this analysis are compared with the results of an asymptotic analysis of the same equation, and the range of applicability of the latter results is specified. It is pointed out that relativistic effects lead to a decrease in the range of frequencies for which instability occurs. For a moderately anisotropic plasma (T⊥/T‖ = 2) relativistic effects lead to an increase in the maximum value of the increment of instability.
This paper gives fast and reliable algorithms for the numerical evaluation of the incomplete gamma functions and for auxiliary functions, such as functions related with the gamma function and error function. All these functions are of basic importance in applied probability problems.
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