Page 771 - Handbook Of Integral Equations

1 σ+i∞ –s
ˆ
ˆ
No Direct transform, f(s) Inverse transform, f(x)= f(s)x ds
2πi σ–i∞


 cosh ν Arcosh(– ln x) –1
28 K ν (s), Re s >0 √ 2 if 0 < x < e ,
ln x – 1
 –1
0 if e < x

1 –1
–1
29 s K ν (s), Re s >0 ν sinh ν Arcosh(– ln x) if 0 < x < e ,
0 if e –1 < x
 √ 2 ν–1/2
π (ln x – 1)
 –1
–ν 1 if 0 < x < e ,
30 s K ν (s), Re s >0, ν > – ν
2 2 Γ(ν +1/2)
 –1
0 if e < x
•
References for Supplement 9: H. Bateman and A. Erd´ elyi (1954), V. A. Ditkin and A. P. Prudnikov (1965).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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