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MathGroup Archive 2007

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Re: Mellin Transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81542] Re: Mellin Transform
  • From: sashap <pavlyk at gmail.com>
  • Date: Wed, 26 Sep 2007 21:45:08 -0400 (EDT)
  • References: <fddemc$9rp$1@smc.vnet.net>

On Sep 26, 6:10 am, "Alexey Nikitin" <niki... at proc.ru> wrote:
>   Dear All,
>
>  Should you tell me please, is it possible to calculate Mellin Transform
> in Wolfram Mathematica?
>
> Alexey.

Hey Alexey,

Mathematica does not have a built-in functionality of MellinTransform,
it has related
LaplaceTransform. You might either use LaplaceTransform to get to the
answer, or
use direct definition in terms of integrate:

In version 6:

In[4]:= MellinTransform[f_, x_, s_, o : OptionsPattern[Integrate]] :=
 Integrate[x^(s - 1) f, {x, 0, Infinity}, o]

In[6]:= MellinTransform[Exp[-a x], x, s,
 Assumptions -> a > 0 \[And] s > 0]

Out[6]= a^-s Gamma[s]

In[8]:= MellinTransform[BesselK[2, x], x, s, Assumptions -> s > 2]

Out[8]= 2^(-2+s) Gamma[-1+s/2] Gamma[1+s/2]

In[10]:= MellinTransform[ArcSin[x], x, s, Assumptions -> -1 < s < 0]

Out[10]= -((\[ImaginaryI] \[ExponentialE]^(-(1/2) \[ImaginaryI] \[Pi]
\
s) Gamma[1-s/2] Gamma[(1+s)/2])/(Sqrt[\[Pi]] s^2))

Hope it helps,
Oleksandr Pavlyk
Special Functions Developer
Wolfram Research



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