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Laplace integral

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An integral of the form

that defines the integral Laplace transform of a function of a real variable , , giving a function of a complex variable . It was considered by P. Laplace at the end of the eighteenth and beginning of the 19th century; it was used by L. Euler in 1737.

Two specific definite integrals depending on the parameters :


Comments

References

[a1] F. Oberhettinger, L. Badii, "Tables of Laplace transforms" , Springer (1973)
[a2] I.N. Sneddon, "The use of integral transforms" , McGraw-Hill (1972) pp. Chapt. 6
[a3] V.A. Ditkin, A.P. Prudnikov, "Integral transforms" , Plenum (1969) (Translated from Russian)
[a4] G. Doetsch, "Handbuch der Laplace-Transformation" , 1–3 , Birkhäuser (1950–1956)
How to Cite This Entry:
Laplace integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Laplace_integral&oldid=32990
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article