Page 748 - Handbook Of Integral Equations

1 c+i∞ px ˜
˜
No Laplace transform, f(p) Inverse transform, f(x)= e f(p) dp
2πi
c–i∞
1 1 √
7 √ exp(a/p) erf a/p √ sinh 2 ax
p πx
1 1 √
8 √ exp(a/p) erfc a/p √ exp –2 ax
p πx

–a x a–1 if 0 < x < b,
9 p γ(a, bp), a, b >0
0 if b < x.
√
10 γ(a, b/p), a >0 b a/2 a/2–1 J a 2 bx
x
–p

11 a γ(p, a) exp –ae –x

0 if 0 < x < a,
12 K 0 (ap), a >0 2 2 –1/2
(x – a ) if a < x.

 0 if 0 < x < a,

13 K ν (ap), a >0 cosh ν Arcosh(x/a)
√ if a < x.
 2 2
x – a
√ 1 a 2
14 K 0 a p exp –
2x 4x
1 √ 1 a 2
15 √ K 1 a p exp –
p a 4x
•
References for Supplement 5: G. Doetsch (1950, 1956, 1958), H. Bateman and A. Erd´ elyi (1954), I. I. Hirschman and
D. V. Widder (1955), V. A. Ditkin and A. P. Prudnikov (1965).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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