(1)
(1)
1
,
0
1
1
1
1
1
()
.
2
2
2
sin
2
i
in
m
mn
n
n
K
ctg
A
e
e
iN
i
n
=
−+
−
+
In the case, when
0
=, SIE (24) can be transformed to the form
(
)
0
0
(1)
1
1
1
0
,
1
()
1
(
)()
1
,
im
mm
CS
CS
F
d
K
F
d
m
e
+
−
=
−
−
(25)
here
(1)
(1)
1
,
0
1
1
1
1
()
.
2
2
2
2
in
m
mn
n
n
K
ctg
A
e
N
i
n
=
−+
+
The obtained SIE (24), (25) are the singular integral equations with the Cauchy
integral kernel [26].
The second boundary condition on the conical strips. Assuming in (1)
2
=,
0
=,
0
=,
12
0
==
,
0
g=
, we come to the second boundary condition on the
strips of the conical gratings:
0
u
n
=
,
(26)
Using a potential continuity
u
in slots, we define the function
()
1
,
mi
U
(3) in the
following form
()
(
)
(
)
(
)
1
(2)
1/2
,,
1/2
(cos)
()
.
(cos)
nN
in
N
i
mi
mn
nN
n
i
P
U
x
e
d
P
d
+
+
+
−+
+
=−
−+
=
=
(27)
Because of application of boundary condition (26) the system of the
functional equations for definition of unknown coefficients
,
mn
x
(
СS
) can be
represented as
0
(2)
,
,,
imN
inN
mn
n
x
e
e
S
+
=−
=
(28)
(
)
(2)
(2)
,,
1
1
0,
,
()
inN
mn
mn
n
n
xe
СS
Nn
n
+
=−
−
=
+
(29)
where
(
)
(
)
(
)
(
)
(
)
1
(2)
2
12
12
1
|
|
(1)
(1/2
(
)
)
(1
)
(
)
(1/2
(
)
)
sin
1
.
cos
cos
nN
n
n
N
n
N
i
i
n
ch
i
n
N
Nn
n
i
n
N
dd
PP
dd
++
++
−
+
−
+
−
+
+
+
−
=
+
+
−
+
−
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