  The multipole resonance probe is one of the recently developed measurement
devices to measure plasma parameter like electron density and temperature based
on the concept of active plasma resonance spectroscopy. The dynamical
interaction between the probe and the plasma in electrostatic, kinetic
description can be modeled in an abstract notation based on functional analytic
methods. These methods provide the opportunity to derive a general solution,
which is given as the response function of the probe-plasma system. It is
defined by the matrix elements of the resolvent of an appropriate dynamical
operator. Based on the general solution a residual damping for vanishing
pressure can be predicted and can only be explained by kinetic effects. Within
this manuscript an explicit response function of the multipole resonance probe
is derived. Therefore, the resolvent is determined by its algebraic
representation based on an expansion in orthogonal basis functions. This allows
to compute an approximated response function and its corresponding spectra,
which show additional damping due to kinetic effects.
