Tables of Integral Transformations - Heat Conduction: Mathematical Models and Analytical Solutions - page 480

Tabl e C. 4 continued

Inverse Image Functions Image Functions

1
√ 2

3 sin

1 αω

αω r 2 δ (

r − α ) , α > 0

4 π

π

2

sin α r 1

ω

[ δ ( ω − α ) − δ ( ω + α )]

r

2
π

1
r

1
ω

2

r − 3 / 2 ω − 3 / 2

2
π

n + 1

n !
ω

α

r n − 1 e − α r , α > 0 , n ≥ 1

α

2

+ ω

2

ω
α

2 m + 1

]
m = 0 ( −

[

2

m C 2 m + 1
n

· 1 )

+ 1

(

r 2 ) γ , 1 − 0 < r < 1

2 γ Γ ( γ + ) ω − γ − 3 / 2 J γ + 3 / 2 ( ω ) , Re γ > − 1 , 1

0 , r > 1

⎨
⎩

2

0 , 0 < r < α

1
ω

1
r √ r 2

J 0 ( αω )

2 ,

r > α

− α