Abstract
In our investigation of the linear theory of waves in plasma and the stability of relativistic beam-plasma systems, we have been led to consider methods for the evaluation of integrals of the form ∫dχ(χ−ζ)−1 exp(−χ2) and ∫dχ(χ−ζ)−1 exp[(1−χ2)−1/2] for complex ζ. In this work, we report on the evaluation of this integral and its derivative by means of continued fraction expansions. The expressions derived allow the precise calculation of these integrals in previously inaccessible regions. Additionally, applications to non-Maxwellian particle distributions, such as those found in the analysis of plasma diodes, are included.
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