Let be the integral:
Int(-oo,oo)dx f(x)exp(iux) I would like to know if there is any method to
evaluate it for u-->oo
-Stationary phase method:=can't be applied since y=x has no "stationary points" for any real x.
- by the way if we had f(x)=g(x)+ih(x) could the integral above be evaluated splitting it into the real and complex part?..thanks.
Int(-oo,oo)dx f(x)exp(iux)=Int(-inf,inf) [g(x)+ih(x)][cos(ux)+isin(ux)] dx
................................ ..=Int(-inf,inf) {[g(x)cos(ux)-h(x)sin(x)]+i[g(x)sin(ux)+h(x)cos(ux)]}dx
....................................=Int(-inf,inf)[g(x)cos(ux)-h(x)sin(x)]dx +
.........................................i.Int(-inf,inf)[g(x)sin(ux)+h(x)cos(ux)]dx
RonL