We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of Bernstein-Szegö type, i.e., weight functions of the form
(
1
−
x
)
α
(
1
+
x
)
β
/
ρ
(
x
)
,
x
∈
(
−
1
,
1
)
{(1 - x)^\alpha }{(1 + x)^\beta }/\rho (x),\quad x \in ( - 1,1)
, where
α
,
β
∈
{
−
1
2
,
1
2
}
\alpha ,\beta \in \{ - \tfrac {1}{2},\tfrac {1}{2}\}
and
ρ
\rho
is a polynomial of arbitrary degree which is positive on
[
−
1
,
1
]
[ - 1,1]
. With the help of this result the norm of the error functional can easily be calculated explicitly for a wide subclass of these weight functions.