  The fits of 0.4 Ca(NO_3)_2 0.6 K(NO_3) (CKN) by schematic mode-coupling
models [V. Krakoviack and C. Alba-Simionesco, J. Chem. Phys. 117, 2161-2171
(2002)] are analyzed by asymptotic expansions. The validity of both the
power-law and the Cole-Cole-peak solutions for the critical spectrum are
investigated. It is found that the critical spectrum derived from the fits is
described by both expansions equally well when both expansions are carried out
up to next-to-leading order. The expansions up to this order describe the data
for 373K over two orders of magnitude in frequency. In this regime an effective
power law omega^a can be identified where the observed exponent $a$ is smaller
than its calculated value by about 15%; this finding can be explained by
corrections to the leading-order terms in the asymptotic expansions. For higher
temperatures, even smaller effective exponents are caused by a crossover to the
alpha-peak spectrum.
