The validity of various approximate formulas that have been proposed for the electron cyclotron emission and absorption at temperatures for which finite-Larmor-radius effects need to be retained to orders higher than the lowest significant one is analyzed in terms of the error of a given approximation with respect to the exact value. An exponential approximation constructed from the two-term series representation of the Bessel functions turns out to be the best one for the relevant (low harmonics) part of the spectrum and for a fairly wide range of temperatures.
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Bornatici et al. (1989) studied this question.
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