  Useful approximation formulae for radiation impedance are given for the
reflection coefficients of both infinitely flanged and unflanged rigid-walled
cylindrical ducts. The expressions guarantee that simple but necessary physical
and mathematical principles are met, like hermitian symmetry for the reflection
coefficient (identical behaviour of positive and negative frequencies) and
causality for the impulse response. A non causal but more accurate expression
is also proposed that is suitable for frequency-domain applications. The
formulae are obtained by analytical and numerical fitting to reference results
from Levine & Schwinger for the unflanged case and extracted from the radiation
impedance matrix given by Zorumski for the infinite flanged case.
