Page 737 - Handbook Of Integral Equations
P. 737
1 c+i∞ px ˜
˜
No Laplace transform, f(p) Inverse transform, f(x)= e f(p) dp
2πi
c–i∞
m ˜
d f(p) m d n m
n
37 p , m ≥ n (–1) x f(x)
dp m dx n
∞ 1
˜
38 f(q) dq f(x)
p x
1 p ∞ f(t)
˜
39 f(q) dq dt
p 0 x t
1 ∞ x f(t)
˜
40 f(q) dq dt
p p 0 t
5.2. Expressions With Rational Functions
1 c+i∞ px ˜
˜
No Laplace transform, f(p) Inverse transform, f(x)= e f(p) dp
2πi
c–i∞
1
1 1
p
1
2 e –ax
p + a
1
3 2 x
p
1 1
4 1 – e –ax
p(p + a) a
1
5 xe –ax
(p + a) 2
p –ax
6 2 (1 – ax)e
(p + a)
1 1
7 2 2 sinh(ax)
p – a a
p
8 2 2 cosh(ax)
p – a
1 1
9 e –bx – e –ax
(p + a)(p + b) a – b
p
1 –ax –bx
10 ae – be
(p + a)(p + b) a – b
1 1
11 2 2 sin(ax)
p + a a
p
12 2 2 cos(ax)
p + a
1 1
13 2 2 e –bx sin(ax)
(p + b) + a a
p b
14 2 2 e –bx cos(ax) – sin(ax)
(p + b) + a a
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
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