Page 175 - Essentials of applied mathematics for scientists and engineers

book Mobk070 March 22, 2007 11:7

165

Appendix B

In this table q = (p/a) 1/2 ; a and x are positive real; α, β, γ are unrestricted; k is a finite integer;
n is a finite integer or zero; v is a fractional number; 1 · 2 · 3 ··· n = n!; 1 · 3 · 5 ··· (2n − 1) =
1
(2n − 1)!! n (n) = (n + 1) = n!; (1) = 0! = 1; (v) (1 − v) = π/ sin vπ; ( ) = π 1/2
2
NO. TRANSFORM FUNCTION
1
1 1
p
1
2 t
p 2
1 t k−1
3
p k (k − 1)!
1 1
4
p 1/2 (πt) 1/2
1
1 t 2
5 2
p 3/2 π
1 2 k k−1/2
6 t
p k+1/2 π 1/2 (2k − 1)!!
1 t v−1
7
p v (v)
1
8 p 1/2 −
t
2π 1/2 5/2
3
3/2
9 p
t
4π 1/2 5/2
k
(−1) (2k − 1)!!
10 p k−1/2
k
t
2 π 1/2 k+1/2
t v−n−1
11 p n−v
(v − n)
1
12 e −α t
p + α
1 e −β t − e −α t
13
(p + α)(p + β) α − β
1
14 te −α t
(p + α) 2