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

**References**:**Erf funcion***From:*Vicent <vginer@gmail.com>