Taking into account (36)-(38), we will express coefficients
()
2
,
mn
y
through
21
()
:
()
()
(
)
2
2
,
,
2
1
1
()
2
in
mn
mn
S
n
y
e
d
n
−
=
−
;
(40)
and for
0
n, respectively,
()
()
2
2
,0
2
,
1
1
1
()
2
sin
i
m
S
m
e
y
d
N
A
=−
−
, where
()
()
()
2
2
,
,
2
,
1
mn
mn
mn
=−
−
.
Using the algorithm given above from (35)-(40), we obtain SIE with Cauchy
kernel for the function
2
()
:
01
2
1
2
1
1
1
()
1
(
)
()
,
,
im
SS
d
K
d
ie
S
+
−
=
−
(41)
with the additional condition
2
()
0
CS
d
=
,
(42)
here
()
()
(
)
1
2
1
1
,
2
0
1
1
1
1
1
(
)
.
2
2
2
sin
2
i
in
mn
n
m
n
i
e
i
K
ctg
e
N
n
A
−
−
−
=
−
−
−
−
−
Numerical realization of the method of discrete singularities for solving the
singular integral equations. Substituting
1
0
=
and
=
we will reduce
integration in (41), (42) on an interval
(
)
1;1
−
:
00
11
2
0
2
0
11
0
1
2
1
1
()
(
)
()
,
1,
1
()
0,
im
dt
K
d
ie
d
−−
−
+
−
=
−
=
(43)
where
0
0
0
11
()
2
2
(
)
K
ctg
−
−
=
−
−
−
()
2
exp
1
1
2
sin
i
m
ie
N
A
−
−
−
()
(
)
0
2
,
0
.
2
in
mn
n
n
i
e
n
−−
−
Here we consider a cone with one slot (
1
N=,
0
=). In this case SIE (43) is
transformed to
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