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Re: Re: Mellin Transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81681] Re: Re: Mellin Transform
  • From: "Alexey Nikitin" <nikitin at proc.ru>
  • Date: Mon, 1 Oct 2007 04:51:28 -0400 (EDT)

Ok. mellinTransform look like rather nice, thank you everybody!
But how about Inverse Laplace transform? Is it possible in Mathematica 
construct  function realizing this kind of integral transform?

Alexey.

----- Original Message -----
From: "Daniel Lichtblau" <danl at wolfram.com>
To: "Alexey Nikitin" <nikitin at proc.ru>
Cc: <mathgroup at smc.vnet.net>
Sent: Wednesday, September 26, 2007 7:22 PM
Subject: [mg81681] Re: [mg81518] Mellin Transform


> Alexey Nikitin wrote:
>>   Dear All,
>>
>>  Should you tell me please, is it possible to calculate Mellin =
Transform
>> in Wolfram Mathematica?
>>
>> Alexey.
>
> 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}]
>
> In[3]:= InputForm[mellinTransform[Sin,z]]
>
> Out[3]//InputForm=
> If[Inequality[-1, Less, Re[z], Less, 1], Gamma[z]*Sin[(Pi*z)/2],
>  Integrate[t^(-1 + z)*Sin[t], {t, 0, Infinity},
>   Assumptions -> Re[z] <= -1 || Re[z] >= 1]]
>
> In[4]:= InputForm[mellinTransform[1/(1+#)&, z]]
>
> Out[4]//InputForm=
> If[Inequality[0, Less, Re[z], Less, 1], Pi*Csc[Pi*z],
>  Integrate[t^(-1 + z)/(1 + t), {t, 0, Infinity},
>   Assumptions -> Re[z] <= 0 || Re[z] >= 1]]
>
> Daniel Lichtblau
> Wolfram Research
>
>



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