<s>
In	O
mathematics	O
,	O
Hadamard	B-Algorithm
regularization	I-Algorithm
(	O
also	O
called	O
Hadamard	B-Algorithm
finite	I-Algorithm
part	I-Algorithm
or	O
Hadamard	B-Algorithm
's	I-Algorithm
partie	I-Algorithm
finie	I-Algorithm
)	O
is	O
a	O
method	O
of	O
regularizing	O
divergent	O
integrals	O
by	O
dropping	O
some	O
divergent	O
terms	O
and	O
keeping	O
the	O
finite	O
part	O
,	O
introduced	O
by	O
.	O
</s>
<s>
exists	O
,	O
then	O
it	O
may	O
be	O
differentiated	O
with	O
respect	O
to	O
to	O
obtain	O
the	O
Hadamard	B-Algorithm
finite	I-Algorithm
part	I-Algorithm
integral	I-Algorithm
as	O
follows	O
:	O
</s>
<s>
Note	O
that	O
the	O
symbols	O
and	O
are	O
used	O
here	O
to	O
denote	O
Cauchy	O
principal	O
value	O
and	O
Hadamard	B-Algorithm
finite-part	I-Algorithm
integrals	I-Algorithm
respectively	O
.	O
</s>
<s>
The	O
Hadamard	B-Algorithm
finite	I-Algorithm
part	I-Algorithm
integral	I-Algorithm
above	O
(	O
for	O
)	O
may	O
also	O
be	O
given	O
by	O
the	O
following	O
equivalent	O
definitions	O
:	O
</s>
<s>
Integral	O
equations	O
containing	O
Hadamard	B-Algorithm
finite	I-Algorithm
part	I-Algorithm
integrals	I-Algorithm
(	O
with	O
unknown	O
)	O
are	O
termed	O
hypersingular	O
integral	O
equations	O
.	O
</s>
