This paper contains graphs and tables of the function
\[
A
i
p
,
q
(
α
,
x
)
=
∫
−
∞
∞
(
2
π
)
−
1
exp
{
i
y
p
/
p
−
α
y
q
/
q
+
i
x
y
}
d
y
A{i_{p,q}}(\alpha ,x) = \int _{ - \infty }^\infty {{{(2\pi )}^{ - 1}}\exp \{ i{y^p}/p - \alpha {y^q}/q + ixy\} \;dy}
\]
and its indefinite integral for
p
=
3
,
5
,
7
p = 3,5,7
, for
q
=
2
,
4
,
6
q = 2,4,6
, and for several values of
α
\alpha
with
α
⩾
0
\alpha \geqslant 0
. It is shown how these tables should influence the choice of an artificial viscosity for a difference scheme for a linear hyperbolic equation.