Page 761 - Handbook Of Integral Equations
P. 761
∞
ˇ
No Original function, f(x) Sine transform, f s (u)= f(x) sin(ux) dx
0
2 arcsin(u/a)
√ if 0 < u < a,
π a – u
2 2
18 Y 0 (ax), a >0 √ 2 2
2 ln u – u – a – ln a
if a < u
√
2
π u – a 2
0 if 0 < u < a,
19 Y 1 (ax), a >0 u
– √ if a < u
a u 2 –a 2
√
2 2
ln u + u + a – ln a
20 K 0 (ax), a >0 √
2
u + a 2
πu
21 xK 0 (ax), a >0 2 2 3/2
2(u + a )
2 –ν–3/2
2
ν
22 x ν+1 K ν (ax), a >0, ν > – 3 √ π (2a) Γ ν + 3 u(u + a )
2 2
•
References for Supplement 7: 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
Page 745
