Dual integral equations of the type
\[
∫
0
∞
u
λ
f
(
u
)
J
μ
(
r
u
)
d
u
=
g
(
r
)
,
0
>
r
>
1
,
∫
0
∞
u
(
u
2
+
a
2
)
−
1
/
2
f
(
u
)
J
v
(
r
u
)
d
u
=
h
(
r
)
,
1
>
r
>
∞
,
\int _0^\infty {{u^\lambda }f\left ( u \right ){J_\mu }\left ( {ru} \right )du = g\left ( r \right ),0 > r > 1, \\ \int _0^\infty u {{\left ( {{u^2} + {a^2}} \right )}^{ - 1/2}}f\left ( u \right ){J_v}\left ( {ru} \right )du = h\left ( r \right ),} 1 > r > \infty ,
\]
where
g
(
r
)
g\left ( r \right )
,
h
(
r
)
h\left ( r \right )
are prescribed functions and
f
(
u
)
f\left ( u \right )
is to be found, are solved exactly by the application of function-theoretic methods. As an example, a closed-form solution is obtained for the diffraction of an electromagnetic wave by a plane slit.