A Hadamard-regularized sum is the finite part remaining after the divergent terms in the asymptotic expansion of a partial sum have been removed. More precisely, if
 |
as 
, where 
is an explicitly specified combination of divergent powers and logarithms of 
, then the Hadamard finite-part prescription assigns
the value 
to 
.
The prescription depends on the chosen cutoff and the terms included in 
, so these data form part of the regularization.
Hadamard regularization is closely related to the Hadamard finite
part used for divergent integrals.
