We derive an indefinite quadrature formula, based on a theorem of Ganelius, for
H
p
H^p
functions, for
p
>
1
p>1
, over the interval
(
−
1
,
1
)
(-1,1)
. The main factor in the error of our indefinite quadrature formula is
O
(
e
−
π
N
/
q
)
O(e^{-\pi \sqrt {N/ q}})
, with
2
N
2 N
nodes and
1
p
+
1
q
=
1
\frac 1 p +\frac 1q=1
. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of
2
\sqrt {2}
in the constant of the exponential. We conjecture that our formula has the best possible value for that constant. The results of numerical examples show that our indefinite quadrature formula is better than Haber’s indefinite quadrature formula for
H
p
H^p
-functions.