<s>
In	O
mathematics	O
,	O
the	O
Nørlund	B-Algorithm
–	I-Algorithm
Rice	I-Algorithm
integral	I-Algorithm
,	O
sometimes	O
called	O
Rice	B-Algorithm
's	I-Algorithm
method	I-Algorithm
,	O
relates	O
the	O
nth	O
forward	B-Algorithm
difference	I-Algorithm
of	O
a	O
function	O
to	O
a	O
line	O
integral	O
on	O
the	O
complex	O
plane	O
.	O
</s>
<s>
It	O
commonly	O
appears	O
in	O
the	O
theory	O
of	O
finite	B-Algorithm
differences	I-Algorithm
and	O
has	O
also	O
been	O
applied	O
in	O
computer	B-General_Concept
science	I-General_Concept
and	O
graph	O
theory	O
to	O
estimate	O
binary	O
tree	O
lengths	O
.	O
</s>
<s>
in	O
1985	O
,	O
is	O
the	O
observation	O
that	O
the	O
resemblance	O
of	O
the	O
Nørlund	B-Algorithm
–	I-Algorithm
Rice	I-Algorithm
integral	I-Algorithm
to	O
the	O
Mellin	O
transform	O
is	O
not	O
accidental	O
,	O
but	O
is	O
related	O
by	O
means	O
of	O
the	O
binomial	O
transform	O
and	O
the	O
Newton	O
series	O
.	O
</s>
<s>
one	O
can	O
then	O
regain	O
the	O
original	O
sequence	O
by	O
means	O
of	O
the	O
Nörlund	B-Algorithm
–	I-Algorithm
Rice	I-Algorithm
integral	I-Algorithm
:	O
</s>
<s>
Very	O
roughly	O
,	O
it	O
can	O
be	O
said	O
to	O
be	O
related	O
to	O
the	O
Nörlund	B-Algorithm
–	I-Algorithm
Rice	I-Algorithm
integral	I-Algorithm
in	O
the	O
same	O
way	O
that	O
Perron	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
is	O
related	O
to	O
the	O
Mellin	O
transform	O
:	O
rather	O
than	O
dealing	O
with	O
infinite	O
series	O
,	O
it	O
deals	O
with	O
finite	O
series	O
.	O
</s>
<s>
The	O
integral	O
representation	O
for	O
these	O
types	O
of	O
series	O
is	O
interesting	O
because	O
the	O
integral	O
can	O
often	O
be	O
evaluated	O
using	O
asymptotic	O
expansion	O
or	O
saddle-point	O
techniques	O
;	O
by	O
contrast	O
,	O
the	O
forward	B-Algorithm
difference	I-Algorithm
series	O
can	O
be	O
extremely	O
hard	O
to	O
evaluate	O
numerically	O
,	O
because	O
the	O
binomial	O
coefficients	O
grow	O
rapidly	O
for	O
large	O
n	O
.	O
</s>
