<s>
In	O
mathematics	O
,	O
and	O
more	O
particularly	O
in	O
analytic	O
number	O
theory	O
,	O
Perron	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
is	O
a	O
formula	O
due	O
to	O
Oskar	O
Perron	O
to	O
calculate	O
the	O
sum	O
of	O
an	O
arithmetic	B-Algorithm
function	I-Algorithm
,	O
by	O
means	O
of	O
an	O
inverse	O
Mellin	O
transform	O
.	O
</s>
<s>
Presume	O
the	O
Dirichlet	O
series	O
to	O
be	O
uniformly	B-Algorithm
convergent	I-Algorithm
for	O
.	O
</s>
<s>
This	O
is	O
nothing	O
but	O
a	O
Laplace	O
transform	O
under	O
the	O
variable	O
change	O
Inverting	O
it	O
one	O
gets	O
Perron	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
.	O
</s>
<s>
The	O
Perron	B-Algorithm
formula	I-Algorithm
is	O
just	O
the	O
special	O
case	O
of	O
the	O
test	O
function	O
for	O
the	O
Heaviside	O
step	O
function	O
.	O
</s>
