Tables of Integral Transformations - Heat Conduction: Mathematical Models and Analytical Solutions - page 477

Tabl e C. 2 countinued

Inverse Image Functions Image Functions

1
s −

1
2

s

sin 2 t

s 2

+ 4

1
s +

1
2

s

cos 2 t

s 2 + 4

2 abs

sin at sin bt

[ s 2

2

][ s 2

2

+( a + b ) +( a − b ) ]

b
( s − a )( s − b )

a −

e at − e bt

( a − b ) s

a e at − b e bt

( s − a )( s − b )

1

J 0 ( α t ) √ s 2

+ α

2

1

I 0 ( α t ) √ s 2

− α

2

γ

α γ
√ α

1

J γ ( α t ) , Re ( γ ) > − 1

+ √ α

2

+ s 2 s 2

2

+ s 2

√ α
s √ s

( √ α

erf t ) , α > 0

+ α

erfc

2 √ t 1

s e − α √ s

, α > 0

e t erfc √ t

1
s + √ s

2
4 t

1
√ π

t e − α

√ s e − α √ s

1

, α ≥ 0

√ π t sin2 √ α t

1

s √ s e − s

1

√ π t cos 2 √ α

1

√ s e − s

1

t