On cylindrical wave functions in media with power law variation in permittivity

When the permittivity of a dielectric medium has a general power-law dependence
\epsilon(\rho) = \epsilon(\rho0)(\rho/\rho0)^{P}
in circularly cylindrical coordinates, the solution takes on a different form, depending on whether or not
p = -2
. This communication is addressed to the problem of showing that the two forms are, in fact, equivalent as
p \rightarrow -2
. The equivalence is made evident through proper choice of the multiplying constant for the case
p \neq -2
.