<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
Gauss	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
quadrature	I-Algorithm
(	O
named	O
after	O
Carl	O
Friedrich	O
Gauss	O
and	O
Carl	O
Gustav	O
Jacob	O
Jacobi	O
)	O
is	O
a	O
method	O
of	O
numerical	B-Algorithm
quadrature	I-Algorithm
based	O
on	O
Gaussian	B-Algorithm
quadrature	I-Algorithm
.	O
</s>
<s>
Thus	O
,	O
Gauss	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
quadrature	I-Algorithm
can	O
be	O
used	O
to	O
approximate	O
integrals	O
with	O
singularities	O
at	O
the	O
end	O
points	O
.	O
</s>
<s>
Gauss	B-Algorithm
–	I-Algorithm
Legendre	I-Algorithm
quadrature	I-Algorithm
is	O
a	O
special	O
case	O
of	O
Gauss	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
quadrature	I-Algorithm
with	O
.	O
</s>
<s>
Similarly	O
,	O
the	O
Chebyshev	B-Algorithm
–	I-Algorithm
Gauss	I-Algorithm
quadrature	I-Algorithm
of	O
the	O
first	O
(	O
second	O
)	O
kind	O
arises	O
when	O
one	O
takes	O
.	O
</s>
<s>
More	O
generally	O
,	O
the	O
special	O
case	O
turns	O
Jacobi	O
polynomials	O
into	O
Gegenbauer	O
polynomials	O
,	O
in	O
which	O
case	O
the	O
technique	O
is	O
sometimes	O
called	O
Gauss	B-Algorithm
–	I-Algorithm
Gegenbauer	I-Algorithm
quadrature	I-Algorithm
.	O
</s>
<s>
Gauss	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
quadrature	I-Algorithm
uses	O
as	O
the	O
weight	O
function	O
.	O
</s>
