<s>
The	O
Andreotti	B-Algorithm
–	I-Algorithm
Norguet	I-Algorithm
formula	I-Algorithm
,	O
first	O
introduced	O
by	O
,	O
is	O
a	O
higher	O
–	O
dimensional	O
analogue	O
of	O
Cauchy	O
integral	O
formula	O
for	O
expressing	O
the	O
derivatives	B-Algorithm
of	O
a	O
holomorphic	O
function	O
.	O
</s>
<s>
Precisely	O
,	O
this	O
formula	O
express	O
the	O
value	O
of	O
the	O
partial	O
derivative	B-Algorithm
of	O
any	O
multiindex	O
order	O
of	O
a	O
holomorphic	B-Architecture
function	I-Architecture
of	I-Architecture
several	I-Architecture
variables	I-Architecture
,	O
in	O
any	O
interior	O
point	O
of	O
a	O
given	O
bounded	B-Algorithm
domain	O
,	O
as	O
a	O
hypersurface	O
integral	O
of	O
the	O
values	O
of	O
the	O
function	O
on	O
the	O
boundary	O
of	O
the	O
domain	O
itself	O
.	O
</s>
<s>
In	O
this	O
respect	O
,	O
it	O
is	O
analogous	O
and	O
generalizes	O
the	O
Bochner	B-Algorithm
–	I-Algorithm
Martinelli	I-Algorithm
formula	I-Algorithm
,	O
reducing	O
to	O
it	O
when	O
the	O
absolute	O
value	O
of	O
the	O
multiindex	O
order	O
of	O
differentiation	O
is	O
.	O
</s>
<s>
When	O
considered	O
for	O
functions	O
of	O
complex	O
variables	O
,	O
it	O
reduces	O
to	O
the	O
ordinary	O
Cauchy	O
formula	O
for	O
the	O
derivative	B-Algorithm
of	O
a	O
holomorphic	O
function	O
:	O
however	O
,	O
when	O
,	O
its	O
integral	B-Algorithm
kernel	I-Algorithm
is	O
not	O
obtainable	O
by	O
simple	O
differentiation	O
of	O
the	O
Bochner	B-Algorithm
–	I-Algorithm
Martinelli	I-Algorithm
kernel	I-Algorithm
.	O
</s>
<s>
The	O
Andreotti	B-Algorithm
–	I-Algorithm
Norguet	I-Algorithm
formula	I-Algorithm
was	O
first	O
published	O
in	O
the	O
research	O
announcement	O
:	O
however	O
,	O
its	O
full	O
proof	O
was	O
only	O
published	O
later	O
in	O
the	O
paper	O
.	O
</s>
<s>
In	O
1977	O
and	O
1978	O
,	O
Lev	O
Aizenberg	O
gave	O
still	O
another	O
proof	O
and	O
a	O
generalization	O
of	O
the	O
formula	O
based	O
on	O
the	O
Cauchy	O
–	O
Fantappiè	O
–	O
Leray	O
kernel	B-Algorithm
instead	O
on	O
the	O
Bochner	B-Algorithm
–	I-Algorithm
Martinelli	I-Algorithm
kernel	I-Algorithm
.	O
</s>
<s>
is	O
a	O
bounded	B-Algorithm
domain	O
whose	O
closure	O
is	O
,	O
</s>
<s>
is	O
the	O
function	B-Algorithm
space	I-Algorithm
of	O
functions	O
holomorphic	O
on	O
the	O
interior	O
of	O
and	O
continuous	O
on	O
its	O
boundary	O
.	O
</s>
<s>
the	O
iterated	O
Wirtinger	O
derivatives	B-Algorithm
of	O
order	O
of	O
a	O
given	O
complex	O
valued	O
function	O
are	O
expressed	O
using	O
the	O
following	O
simplified	O
notation	O
:	O
</s>
<s>
For	O
every	O
multiindex	O
,	O
the	O
Andreotti	O
–	O
Norguet	O
kernel	B-Algorithm
is	O
the	O
following	O
differential	O
form	O
in	O
of	O
bidegree	O
:	O
</s>
