
28.3. Tables of Fourier Cosine Transforms 1483
No. Original function, f(x)
Cosine transform,
ˇ
f
c
(u) =
Z
∞
0
f(x) cos(ux) dx
5
1
a
2
− x
2
, a > 0
π sin(au)
2u
6
a
a
2
+ (b + x)
2
+
a
a
2
+ (b − x)
2
πe
−au
cos(bu)
7
b + x
a
2
+ (b + x)
2
+
b − x
a
2
+ (b − x)
2
πe
−au
sin(bu)
8
1
a
4
+ x
4
, a > 0
1
2
πa
−3
exp
−
au
√
2
sin
π
4
+
au
√
2
9
1
(a
2
+ x
2
)(b
2
+ x
2
)
, a, b > 0
π
2
ae
−bu
− be
−au
ab(a
2
− b
2
)
10
x
2m
(x
2
+ a)
n+1
,
n, m = 1, 2, . . . ; n + 1 > m ≥ 0
(−1)
n+m
π
2n!
∂
n
∂a
n
a
1/
√
m
e
−u
√
a
11
1
√
x
r
π
2u
12
1
√
x
if 0 < x < a,
0 if a < x
2
r
π
2u
C(au), C(u) is the Fr esnel integral
13
0 if 0 < x < a,
1
√
x
if a < x
r
π
2u
1 − 2C(au)
, C(u) is the Fresnel integral
14
0 if 0 < x < a,
1
√
x − a
if a < x
r
π
2u
cos(au) −sin(au)
15
1
√
a
2
+ x
2
K
0
(au)
16
1
√
a
2
− x
2