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.
