Environmental Engineering Reference
In-Depth Information
Tabl e C. 2 countinued
Inverse Image Functions
Image Functions
1
π
t sin 1
s e s sin s
1
2 t
1
π
t cos 1
s e s cos s
1
2 t
e ( ξ ξ ) s 2
erf s
I 0 c t 2
2 H
α t
1
π t sin
c 2
( ξ ξ )
( ξ ξ )]
(
2
)
[
t
s 2
c 2
Tabl e C. 3 Hankel Transformations
Inverse Image Functions
Image Functions
+
+
f ( ω ) J 0 ( ω r )
f ( ω )=
f ( r )=
ω
rf ( r ) J 0 ( ω r ) d r
0
0
1
,
r
< α
α
ω
f ( r )=
J 1 ( αω )
0
,
r
> α
α
2
2
r 2
4
α
ω
2
α
,
r
< α
3 J 1 ( αω )
2 J 0 ( αω )
0
,
r
> α
ω
e α r
r
1
ω
2
+ α
2
1
sin
α
r
α
2 , 0 < ω < α
,
α >
0
2
ω
r
0
,
ω > α
1
cos
α
r
ω
2 , ω > α
,
α >
0
2
α
r
0
,
0
< ω < α
1
r δ (
1
r
α )
J 0
( αω )
 
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