<s>
In	O
mathematical	O
analysis	O
,	O
Darboux	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
is	O
a	O
formula	O
introduced	O
by	O
for	O
summing	O
infinite	O
series	O
by	O
using	O
integrals	O
or	O
evaluating	O
integrals	O
using	O
infinite	O
series	O
.	O
</s>
<s>
It	O
is	O
a	O
generalization	O
to	O
the	O
complex	O
plane	O
of	O
the	O
Euler	B-Algorithm
–	I-Algorithm
Maclaurin	I-Algorithm
summation	I-Algorithm
formula	I-Algorithm
,	O
which	O
is	O
used	O
for	O
similar	O
purposes	O
and	O
derived	O
in	O
a	O
similar	O
manner	O
(	O
by	O
repeated	O
integration	O
by	O
parts	O
of	O
a	O
particular	O
choice	O
of	O
integrand	O
)	O
.	O
</s>
<s>
Darboux	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
can	O
also	O
be	O
used	O
to	O
derive	O
the	O
Taylor	O
series	O
from	O
calculus	O
.	O
</s>
<s>
Taking	O
φ	O
to	O
be	O
a	O
Bernoulli	O
polynomial	O
in	O
Darboux	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
gives	O
the	O
Euler	B-Algorithm
–	I-Algorithm
Maclaurin	I-Algorithm
summation	I-Algorithm
formula	I-Algorithm
.	O
</s>
