In this paragraph the K and EC formulae will be presented in detail, in order to facilitate the use of the following tables. The definitions that follow are taken from Tinsley (1970).
Consider a galaxy at a redshift z, observed at the present epoch 
,
whose light was emitted at the time 
.
Let's define 
as the monochromatic luminosity
measured at the wavelength 
at the time t in its rest frame,
in units 
or equivalent.
is defined as the observed luminosity
in the band with effective wavelength
(in 
):
where 
is the transmission function of the instrument and
is the observed monochromatic flux
(
) at the wavelength 
.
Then the following equation is valid:
being D the luminosity distance.
Equation (2) can be written as:
The term in the square brackets is the K correction and the last term is
the evolutionary correction.
From Eq. (3) the observed magnitude
for the band with effective wavelength 
is equal to the sum of five terms:
a) the absolute magnitude in the same band as it would be measured in the rest
frame at the epoch of observation 
. This is indicated as
and corresponds to the numerator of the first term in
the Eq. (2);
b) a term that only depends on the luminosity distance D;
c) a constant term, depending only on the band used, that determines the normalization of the absolute magnitude;
d) the K correction;
e) the evolutionary EC correction.
The K correction is the difference between the observed magnitude
of the galaxy of age
measured at the wavelength 
and the magnitude of the same galaxy
of age 
computed at
.
Notice that 
is the moment of observation
(
15 Gyr), while 
is the time at which the light has been emitted.
Therefore the K correction corresponds to the difference in
magnitude of two objects with identical spectrum due to the redshift:
it does not include in any way the intrinsic evolution of the spectrum
due to the evolution of the stellar populations that contribute to it.
On the contrary, the EC correction depends on the intrinsic evolution
of the spectral energy distribution (SED),
being the difference between the magnitude of a galaxy of age
and the same galaxy evolved (whose spectrum is different from
the one of the previous galaxy)
of age 
, both computed at
. It is therefore the difference in absolute magnitude
measured in the rest frame of the galaxy at the wavelength of emission.
The sum of the K and EC corrections is the difference between
the magnitude of a galaxy of age
redshifted and the one of the evolved galaxy
observed at the time 
at z=0.
Both corrections are computed on the basis of models of
spectrophotometric evolution,
assuming a star formation history for each morphological type and having fixed
the cosmological parameters.
In the general case 
it is valid
where t is the look-back time,
is the Hubble constant, 
is the deceleration
parameter and z is the redshift.
The tables have been computed
for 
and 
,
corresponding to an age of the Universe 
Gyr.
Corrections for different cosmological parameters can be computed
directly from the evolving SEDs presented in Tables 6-29.
If one prefers to define the corrections with respect to the observed
SED of a given galaxy, the adopted model present-day SEDs given in Tables 3-5
can be replaced with the observed SED.