Re: Mellin Transform
- To: mathgroup at smc.vnet.net
- Subject: [mg81582] Re: Mellin Transform
- From: chuck009 <dmilioto at comcast.com>
- Date: Fri, 28 Sep 2007 02:13:23 -0400 (EDT)
Then I'd numerically integrate the transform to recover the function (don't forget the i):
fhat[x_] := (1/(2*Pi*I))*NIntegrate[
I*((Gamma[z]*Sin[Pi*(z/2)])/x^z) /.
z -> 0.2 + I*y, {y, -100, 100}]
stable = Table[{x, fhat[x]},
{x, 0.001, 2*Pi, 0.1}]
ListPlot[stable]
Pretty close for my money :)
>
> Could use the definition as an integral.
>
> http://mathworld.wolfram.com/MellinTransform.html
>
> In[1]:= mellinTransform[f_,z_] :=
> Integrate[f[t]*t^(z-1), {t,0,Infinity}]
>