Page 733 - Handbook Of Integral Equations

∞

˜
No Original function, f(x) Laplace transform, f(p)= e –px f(x) dx
0
2 2 2
p p + a + b
20 cos(ax) cos(bx)
2
2
p +(a + b) 2 p +(a – b) 2
ax cos(ax) – sin(ax) a
21 p arctan – a
x 2 x
a
22 e bx sin(ax) 2 2
(p – b) + a
p – b
23 e bx cos(ax)
(p – b) + a 2
2
2
2a p
24 sin(ax) sinh(ax)
4
p +4a 4
2 2
a p +2a
25 sin(ax) cosh(ax)
4
p +4a 4
2 2
a p – 2a
26 cos(ax) sinh(ax)
p +4a 4
4
p 3
27 cos(ax) cosh(ax)
4
p +4a 4
4.7. Expressions With Special Functions
∞

˜
No Original function, f(x) Laplace transform, f(p)= e –px f(x) dx
0
1 2 2 1
1 erf(ax) exp b p erfc(bp), b =
p 2a
√
√ a
2 erf ax √
p p + a
√
√ a
ax
3 e erf ax √
p (p – a)
√
1
1
4 erf a/x 1 – exp – ap
2 p
√ √
√ p + a – a
5 erfc ax √
p p + a
√ 1
ax
6 e erfc ax √
p + ap
1
√
1
7 erfc a/x exp – ap
2 p
1 2
8 Ci(x) ln(p +1)
2p
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 717