A Joint Fourier - Laplace Inversion

*To*: mathgroup at smc.vnet.net*Subject*: [mg100592] A Joint Fourier - Laplace Inversion*From*: pcoords29 at gmail.com*Date*: Tue, 9 Jun 2009 03:52:36 -0400 (EDT)

Dear MathGroup, I am trying to work out numerically the inverse Fourier - Laplace transform of a function , F[q,s], (where q & s are the Fourier and Laplace parameters respectively), for various given values of x & t. f (x, t) is the joint inverse of F[q, s]. I already have the code for doing the numerical inversion of a Laplace transform; it needs to be fed a function of s and a t value. Hence I first carry out the Fourier inversion numerically with NIntegrate, hoping to get the function of s to feed into the Laplace inversion routine (InvLap) This is my attempt IFL[F_, x_?NumericQ, t_?NumericQ]:= Module[ {g}, g[s_?NumericQ]:= 1/(2Pi) NIntegrate[F*Exp[I q x],{q,-Infinity, Infinity}] InvLap[g,t] ] I 'd like IFL[F[q,s], 3.5, 2.1] to give me f (3.5, 2.1), but it doesn't ! I can't suss out how to get the g[s] function. Could you please help. Thanks in advance. Regards. Sid