ABSTRACT
F (s)
20. erf ( a
2 √ t
) 1− e−a√s s
21. erfc ( a
2 √ t
s
22. f(t) with period = T † ∫ T 0 e−st f(t) dt 1− e−Ts
23. J0(at) 1√
s2 + a2
24. I0(at) 1√
s2 − a2
25. Jn(at) 1√
s2 + a2
( a
s + √ s2 + a2
)n , n > −1
26. In(at) 1√
s2 − a2 (
a
s + √ s2 − a2
)n , n > −1
27. t J1(at) a
(s2 + a2)3/2 , a > 0
28. t I1(at) a
(s2 − a2)3/2 , a > 0
29. † tn Jn(at) (2n)! an
2n n! (√
s2 + a2 )2n+1 , n > −1/2
30. † tn In(at) 2n√ π
Γ(n + 1/2) an (√
s2 − a2 )2n+1 , n > −1/2
31. t J0(at) s
(s2 + a2)3/2 , a > 0
32. t I0(at) s
(s2 − a2)3/2 , a > 0
f(t) L{f(t)} = F (s) = f¯(s)
33. (t− a) µ−1
Γ(µ) H(t− a) e
sµ , µ > 0
34. ( t a
)(µ−1)/2 Jµ−1
( 2 √ at
) e−a/s
sµ , µ > 0
35. ( t a
)(µ−1)/2 Iµ−1
( 2 √ at
) ea/s
sµ , µ > 0
36. cos 2 √ at√
π t
e−a/s√ s
, a > 0
37. sin 2 √ at√
π a
e−a/s
s3/2 , a > 0
38. e −a2/4t √ π t
√ s
, a > 0
39. ae −a2/4t
2 √ π t3
e−a √ s, a > 0
40. e −bt − e−at
t ln
(s + a s + b
) , a, b > 0
41. δ(t) 1
42. δ(t− a) e−as, a > 0
† Note that {s} > ∣∣ {a}∣∣ (in 29), and {s} > ∣∣{a}∣∣ (in 30).
