Bilateral Laplace Transform

Author

Eric W. Weisstein
April 4, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegralTransforms/BilateralLaplaceTransform.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BilateralLaplaceTransform.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

LaplaceTransform2[f_,t_,s_,opts___]:=Integrate[Exp[-s t]f,{t,-∞,∞},opts]

Table

fns={1,t,t^n,Exp[a t],Cos[ω t],Sin[ω t],Cosh[ω t],Sinh[ω t],Exp[a t]Sin[b t],Exp[a t]Cos[b t],DiracDelta[t-c],UnitStep[t-c],BesselJ[0,t],BesselJ[n,t]};

{#,FullSimplify[LaplaceTransform2[#,t,s,GenerateConditions->False]]}&/@fns//TableForm//TraditionalForm