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Corollary 8.5 (Power series (1 +
x
)
y
, reformulation 3).
E
2
cos
2
Δ
)
−
3
/
2
=
(1
−
=1+
3
4
E
2
+
45
64
E
4
+
175
256
E
6
+O
1
(
E
8
)+
(8.36)
+
3
512
E
6
+O
2
(
E
8
)
cos 2
Δ
+
4
E
2
+
15
16
E
4
+
525
+
15
256
E
6
+O
3
(
E
8
)
cos 4
Δ
+
35
512
E
6
+O
4
(
E
8
)
64
E
4
+
105
cos 6
Δ
+O
5
(
E
8
)
.
End of Corollary.
Corollary 8.6 (Power series (1 +
x
)
y
, multiplication with (1
− E
2
)).
E
2
)(1
E
2
cos
2
Δ
)
−
3
/
2
=
(1
−
−
1
3
5
4
E
2
64
E
4
256
E
6
+O
1
(
E
8
)+
=1
−
−
−
(8.37)
+
3
512
E
6
+O
2
(
E
8
)
cos 2
Δ
+
4
E
2
+
3
16
E
4
+
45
+
15
256
E
6
+O
3
(
E
8
)
cos 4
Δ
+
35
512
E
6
+O
4
(
E
8
)
64
E
4
+
45
cos 6
Δ
+O
5
(
E
8
)
.
End of Corollary.
Corollary 8.7 (Termwise integration of uniformly convergent series).
cos
nx
d
x
=
1
n
sin
nx ∀n ∈
Z
,
Δ
(1
− E
2
)(1
− E
2
cos
2
Δ
)
−
3
/
2
d
Δ
=
0
=
1
−
256
E
6
+O
1
(
E
8
)
Δ
+
1
3
5
4
E
2
64
E
4
−
−
(8.38)
+
3
1024
E
6
+O
2
(
E
8
)
sin 2
Δ
+
8
E
2
+
3
45
32
E
4
+
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