At the same time estimation
2
(2)
,
22
sin
()
mn
O
Nn
=
+
is true for
(2)
,
mn
, when
(
)
1
Nn
+
.
After introducing coefficients
(2)
,
mn
y
:
0
(2)
(2)
,,
m
mn
mn
n
yx
=−
, we rewrite the system
(28), (29) in the form:
(2)
,
0,
in
mn
n
y
e
S
+
=−
=,
(30)
(
)
(
)
0
0
(2)
(2)
,,
(2)
0
,
00
1
1
()
1
1
,
.
()
in
mn
mn
n
im
mm
n
ye
Nn
n
m
e
СS
Nm
m
+
=−
−=
+
=−
−
+
(31)
Let us consider the function
(2)
2,
()
in
mn
n
ye
+
=−
=
,
,
−
.
(32)
Taking into account (30), we have
(2)
,2
1
()
2
in
mn
CS
y
e
d
−
=
. Using the
algorithm given for the first boundary condition problem, we will reduce system (30),
(31) to SIE with respect to the required function
2
()
(32):
0
0
(2)
2
2
,
1
1
ˆ(
)
()
(
)
()
2
2
,,
m
CS
CS
im
m
F
d
K
d
f
e
CS
−
+
−
=
=−
(33)
(2)
(2)
2
(
)
(
)
mm
KK
−
=−
−
,
(2)
(
)
2
,
0
1
()
()
in
mn
n
n
K
e
Nn
n
−
−=
+
,
(
)
0
0
(2)
0
,
,
00
1
1
()
m
mm
m
f
Nm
m
=−
+
,
(2)
,0
m
f
=
.
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