Laplace Transform

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Auxiliary Sections > Integral Transforms > Tables of Laplace Transforms > Laplace Transforms: Expressions
with Error Functions
Laplace Transforms: Expressions with Error Functions
Z
Laplace transform, fe(p) =
Original function, f (x)
No
1
erf(ax)
2
erf
3
eax erf
4
erf
5
erfc
6
¡√ ¢
eax erfc ax
7
erfc
¡√
¢
ax
¡√
ax
¡1p
a/x
2
¡√
ax
¡1p
2
¢
¡
1
exp b2 p2 erfc(bp),
p
√
a
√
p p+a
√
a
√
p (p − a)
¢
0
e−px f (x) dx
1
2a
¡ √ ¢¤
1£
1 − exp − ap
p
√
√
p+a− a
√
p p+a
¢
¢
a/x
b=
∞
p+
1
√
ap
¡ √ ¢
1
exp − ap
p
¢
Notation: erf z is the error function and erfc z is the complementary error function.
References
Bateman, H. and Erdélyi, A., Tables of Integral Transforms. Vols. 1 and 2, McGraw-Hill Book Co., New York, 1954.
Doetsch, G., Einführung in Theorie und Anwendung der Laplace-Transformation, Birkhäuser Verlag, Basel–Stuttgart, 1958.
Ditkin, V. A. and Prudnikov, A. P., Integral Transforms and Operational Calculus, Pergamon Press, New York, 1965.
Polyanin, A. D. and Manzhirov, A. V., Handbook of Integral Equations , CRC Press, Boca Raton, 1998.
Laplace Transforms: Expressions with Error Functions
c 2005 Andrei D. Polyanin
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