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Re: Mellin Transform

• To: mathgroup at smc.vnet.net
• Subject: [mg81551] Re: [mg81518] Mellin Transform
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 26 Sep 2007 21:49:45 -0400 (EDT)
• References: <200709261046.GAA09299@smc.vnet.net>

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

• References:
  • Mellin Transform
    • From: "Alexey Nikitin" <nikitin@proc.ru>