  The impedance for a monopole antenna is derived and compared with the cases
for wire dipole and double-sphere antennas. This derivation produces a new
expression for the monopole antenna response function, $F_{m1}(x)$. The
monopole, wire dipole, and double-sphere response functions are compared by
modeling an antenna in Earth's ionospheric plasma (i.e. electrostatic and
collisionless) and predicting the antenna capacitance and voltage power spectra
for quasi-thermal noise (QTN) and shot noise. The monopole antenna current
distribution is assumed to be a half-triangular current distribution
(considering only the positive half of the triangular distribution). The
predictions for the shot noise and capacitance presented problems, as the
integral over wavenumber-space or $k$-space did not converge for large values
of $k$. The derived expression therefore remains a current problem and
necessitates future work to determine a more general expression. In this paper
we bring the problem of an appropriate analytic monopole antenna response
function to the attention of the community and outline a number of tests that
can be used to verify any future expression.
