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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}]
>


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