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Re: Erf funcion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123952] Re: Erf funcion
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Mon, 2 Jan 2012 02:44:53 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201201010729.CAA28444@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

You can eliminate Erf this way:

Clear[FiX]
rule = Erf[x_] :> 2*FiX[x*Sqrt[2]] - 1;
expr = 3 (2^(7/2 - 2 (k + t))) Cp (E^(-d^2 - (36 Cp^2)/lambda^2))
((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] +
      Erf[(6 Cp + d lambda)/(Sqrt[2] lambda)])^k);
expr /. rule // Simplify

3 2^(7/2 - 2 (k + t)) Cp E^(-d^2 - (36 Cp^2)/lambda^2)

3 2^(7/2 - 2 (k + t)) Cp E^(-d^2 - (36 Cp^2)/lambda^2)

but as you can see, for this expression it makes no difference.

Are you also trying to eliminate the exponential function?

Bobby

On Sun, 01 Jan 2012 01:29:27 -0600, Vicent <vginer at gmail.com> wrote:

> Hello.
>
> I have an expression that depends on the Cumulative Distribution
> Function (CDF) of a Normal Variable with mean = 0 and standard
> deviation = 1.
>
> When I perform operations and/or derivatives with/for that function
> with Mathematica, I get expressions involving Erf function, as the CDF
> function of a Normal distributed variable and Erf (error function) are
> closely related. Concretely,
>
>     FiX[x] == (1/2)*(1 + Erf[x/Sqrt[2]])
>
> and thus
>
>     Erf[x] == 2*FiX[x*Sqrt[2]] - 1
>
> where FiX stands for the previously mentioned CDF, I mean:
>
>     X = NormalDistribution[0, 1]
>     FiX[x_] := CDF[X, x]
>
>
> Is there a quick way to ask Mathematica not to use  Erf  but always
> let the results as a function of FI[x]??
>
> The expressions I get as a result of my computations are larger than
> this short example:
>
>     3 (2^(7/2 - 2 (k + t))) Cp (  E^(-d^2 - (36 Cp^2)/lambda^2))
> ((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] + Erf[(6 Cp + d lambda)/(Sqrt[2]
> lambda)])^k)
>
> where "Cp", "k", "t", "d" and "lambda" are parameters or arguments
> that I want to keep as "generic".
>
> So, how can I "translate" expressions such as the last one into "FiX
> mode"? Or, better, how can I prevent Mathematica to reduce everything
> to "Erf mode"??
>
> I hope my question is clear enough... :)
>
> Thank you very much in advance for your answers.
>
> And have a good new year!
>
>
> --
> vicent
> dooid.com/vicent
>


-- 
DrMajorBob at yahoo.com



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