Page 739 - Handbook Of Integral Equations

1 c+i∞ px ˜
˜
No Laplace transform, f(p) Inverse transform, f(x)= e f(p) dp
2πi
c–i∞
p 2 1 –ax 2 ax/2 1 √
35 3 e + e cos(kx), k = a 3
3
2
3
p + a 3
1 e –ax – e –bx cos(cx)+ ke –bx sin(cx) a – b
36 2 2 , k =
p + a) (p + b) + c ] (a – b) + c 2 c
2
–ae –ax + ae –bx cos(cx)+ ke –bx sin(cx)
p 2 2 ,
37 2 2 (a – b) + c
p + a) (p + b) + c ] b + c – ab
2
2
k =
c
2
2
2 –ax
a e +(b +c –2ab)e –bx cos(cx)+ke –bx sin(cx)
p 2 2 2 ,
38 2 (a–b) +c
3
2
2
p + a) (p + b) + c ] ab – b
k = –ac – bc +
c
1 1 3
39 6 x
p 4
1 1 1 1 1
2
40 – x + x – e –ax
p (p + a) a 3 a 2 2a a 3
3
1 1 2
41 x 1+ e –ax + e –ax – 1
p (p + a) 2 a 2 a 3
2
1 a + b 1 1 –ax 1 –bx
42 – + x + e + e
2 2
2
2
2
p (p + a)(p + b) a b ab a (b – a) b (a – b)
1 1 –ax 2 –bx 2
43 2 2 2 e x + + e x –
(p + a) (p + b) (a – b) a – b a – b
1 1 3 –ax
44 4 6 x e
(p + a)
p
1
2 –ax
3 –ax
45 4 1 2 x e – ax e
6
(p + a)
1 1
46 2 2 2 ax – sin(ax)
p (p + a ) a 3
1 1
47 4 4 sinh(ax) – sin(ax)
p – a 2a 3
p
48 4 4 1 cosh(ax) – cos(ax)
p – a 2a 2
p 2 1
49 sinh(ax) + sin(ax)
4
p – a 4 2a
p 3 1
50 cosh(ax) + cos(ax)
4
p – a 4 2
1 1 ax
51 √ cosh ξ sin ξ – sinh ξ cos ξ , ξ = √
p + a 4 a 3 2 2
4
p 1 ax ax
52 4 4 sin √ sinh √
p + a a 2 2 2
p 2 1 ax
53 √ cos ξ sinh ξ + sin ξ cosh ξ , ξ = √
4
p + a 4 a 2 2
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
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