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
)
dω
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
2π
r
δ
(
1
2π
r
−
α
)
J
0
(
αω
)
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