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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