Environmental Engineering Reference
In-Depth Information
Tabl e C. 1 continued
Inverse Image Functions
Image Functions
√ 2
1
π
| ω |
|
x
|
2cos 2 ch 2
ch
ch
α
x
x , − π < α < π
ch
π
ω +
cos
α
sh
x
shπ x , − π < α < π
α
α
chω + cos α
sin
sin 2 sh 2
chω + cos α
sh
x
chπ x ,
α
| α | < π
2i
⎧
⎨
⎩
1
√ α
x 2 , |
x
| < α
π J 0 ( α | ω | )
2
−
0
,
|
x
| > α
δ ( x )
1
1
2πδ ( ω )
π P i
d
Polynomial P ( x )
2
δ ( ω )
d
ω
δ ( m ) (
m
x
)
(
i
ω )
e bx
2
πδ ( ω +
i b
)
sin bx
i
π [ δ ( ω +
b
) − δ ( ω −
b
)]
cos bx
π [ δ ( ω +
b
)+ δ ( ω −
b
)]
sh bx
π [ δ ( ω +
i b
) − δ ( ω −
i b
)]
ch bx
π [ δ ( ω +
i b
)+ δ ( ω −
i b
)]
1
π
α
e − α | ω |
+ x 2 ,
Re ( α ) < 0
2
α
x
i
ωπ
2
e α | ω |
2 ,
Re ( α ) < 0
α
( α
2
+
x 2
)
 
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