<s>
In	O
mathematics	O
,	O
Gosper	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
due	O
to	O
Bill	O
Gosper	O
,	O
is	O
a	O
procedure	O
for	O
finding	O
sums	O
of	O
hypergeometric	O
terms	O
that	O
are	O
themselves	O
hypergeometric	O
terms	O
.	O
</s>
<s>
That	O
is	O
:	O
suppose	O
one	O
has	O
a(1 )	O
+	O
...	O
+	O
a(n )	O
=	O
S(n )	O
S(0 )	O
,	O
where	O
S(n )	O
is	O
a	O
hypergeometric	O
term	O
(	O
i.e.	O
,	O
S( n+1	O
)	O
/S	O
( n	O
)	O
is	O
a	O
rational	O
function	O
of	O
n	O
)	O
;	O
then	O
necessarily	O
a(n )	O
is	O
itself	O
a	O
hypergeometric	O
term	O
,	O
and	O
given	O
the	O
formula	O
for	O
a(n )	O
Gosper	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
finds	O
that	O
for	O
S(n )	O
.	O
</s>
<s>
Gosper	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
can	O
be	O
used	O
to	O
discover	O
Wilf	O
–	O
Zeilberger	O
pairs	O
,	O
where	O
they	O
exist	O
.	O
</s>
<s>
Then	O
feed	O
a(k )	O
:=	O
F( n+1	O
,	O
k	O
)	O
F(n,k )	O
into	O
Gosper	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Gosper	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
finds	O
(	O
where	O
possible	O
)	O
a	O
hypergeometric	O
closed	O
form	O
for	O
the	O
indefinite	O
sum	O
of	O
hypergeometric	O
terms	O
.	O
</s>
<s>
Bill	O
Gosper	O
discovered	O
this	O
algorithm	O
in	O
the	O
1970s	O
while	O
working	O
on	O
the	O
Macsyma	B-Language
computer	O
algebra	O
system	O
at	O
SAIL	O
and	O
MIT	O
.	O
</s>
