, for a finite time series we use the integral:
To obtain the generalized fractal dimensions, , for a finite time series we use the integral:
,
where 
is the Heaviside function: 
, if 
and 
for 
.
We then look for a stable region of 
as the value for , though we have allowed other methods for this calculation.
In this fashion, D0 represents the box counting or capacity dimension, D1, the information dimension and D2 the correlation dimension.
The particular case, 
, can be obtained by the L’Hôpital rule and yields the definition of the information dimension:
.