Geography Reference
In-Depth Information
f (0) = 0 = c
(23.24)
f ( V )= 23
16 tanhV + 1
7
1
48 tanh 3 V
80 tanh 5 V + O 7 ( tanhV )
16 V
(23.25)
Box 23.11 (The integral 1+ tanh 2 xdx ).
1+ x 2 =1+ 1
1
2 ·
1
4 x 4 + 1
1
4 ·
3
6 ·
2 x 2
x 6 +0 8 ,
2 ·
∀|
x
|
< 1
(23.26)
1+ tanh 2 x =1+ 1
1
8 tanh 4 x + 1
2 tanh 2 x
16 tanh 6 x + O 8 ( tanhx ) ,
∀|
tanh x
|
< 1
(23.27)
tanh 2 xdx = −tanhx + x
(23.28)
tanh 4 xdx =
3 tanh 3 x + tanh 2 xdx =
1
1
3 tanh 3 x
tanhx + x
(23.29)
tanh 6 xdx =
5 tanh 5 x + tanh 4 xdx =
1
1
1
5 tanh 5 x −
3 tanh 3 x
tanhx + x
(23.30)
1+ tanh 2 xdx = x 1+ 1
tanhx 1
+
1
8 + 1
1
8 + 1
2
2
(23.31)
16
16
3 tanh 3 x 1
1
1
16
1
80 tanh 5 x + O 7 ( tanhx )
8
2 :=
2 onto the
Box 23.12 (Equiareal mapping of the rotational symmetric hyperboloid
M
H
circular cylinder
C
1 ).
f =cosh V cosh 2 V = 1+ tanh 2 h
Λ 1 Λ 2 ( V )=1
V
1 − tanh 2 h
(23.32)
f ( V )= (1
tanh 2 V ) 1 1+ tanh 2 V 1 / 2 dV
(23.33)
f (0) = 0 = c
(23.34)
f ( V )= 85
69
16 tanhV
45
23
48 tanh 3 V
80 tanh 5 V + O 7 ( tanhV )
16 V
(23.35)
tanh 2 x 1 1+ tanh 2 xdx ).
Box 23.13 (The integral 1
1
x 2 1 1+ x 2 =1+ 3
2 x 2 + 11
8 x 4 + 23
16 x 6 + O 8 ∀|
x
|
< 1
(23.36)
 
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