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MathGroup Archive 2007

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Re: Limit of Error function Erf

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73570] Re: Limit of Error function Erf
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Thu, 22 Feb 2007 04:29:50 -0500 (EST)
  • References: <ergpqn$hbq$1@smc.vnet.net>

Hi Ben.

It would be very good to post your queries with the Mathematica inputs/
outputs
in InputForm.
A quick way to do that is by simply selecting the Cells and press Shift
+Ctrl+I.

Here is your (?, if I understood well) function

f[a_, t_] := Erf[1/Sqrt[a*t]]

Here is its behavior w.r.t. t and a (for possitive values of both the
variable and the parameter).

(Plot[f[#1, t], {t, 0, 20}, PlotStyle -> AbsoluteThickness[2], Axes ->
False, Frame -> {True, True, False, False},
     PlotRange -> {{-0.01, 20.02}, {-0.01, 1.02}}, PlotLabel -> " a =
"NumberForm[#1, {4, 2}, NumberPadding -> {"0", "0"}],
     TextStyle -> {FontSize -> 14, FontFamily -> "Times"}] & ) /@
Range[0.5, 10, 0.5];
SelectionMove[EvaluationNotebook[], All, GeneratedCell];
FrontEndTokenExecute["CellGroup"];
FrontEndTokenExecute["OpenCloseGroup"];

Note also

<< "NumericalMath`NLimit`"
(NLimit[f[#1, z], z -> Infinity, Terms -> 30, WorkingPrecision -> 40]
& ) /@ Range[10]

{-8.716924561433210486410936266571876625`24.29557956276237*^-12,
  -1.269275660096993061044545254729341002`23.672436370455248*^-12,
  -2.86213569331613466882254063714466158`23.079703797051316*^-13,
  -4.3828770303475029188837881665772226`22.273459290696994*^-14,
3=2E2217955602193993240763347697441065`22.13952029101826*^-14,
  5.7599600309850567850382333549004589`22.421383458426906*^-14,
6=2E4801395943535415032619770496493483`22.5834664699494*^-14,
  6.4912088408225900313727551447536176`22.599662616855426*^-14,
6=2E2215385073249535229051137148001572`22.593986272913366*^-14,
  5.8500495991844001124169155219126662`22.678503185217146*^-14}

(Limit[f[#1, z], z -> Infinity] & ) /@ Range[10]
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

Limit[Erf[z], z -> 0]
0

So, you have encountered a bug, I also believe.


Dimitris


=CF/=C7 ben =DD=E3=F1=E1=F8=E5:
> Dear group
>
> I dont understand the following behaviour of Mathematica,
> I would say the first result is simply wrong
>
> 1.)
>
> Limit[Erf[1\/Sqrt[\[Alpha]\ t]], t -> \[Infinity],
>     Assumptions -> {\[Alpha] > 0}]
>
> gives infinity
>
> 2.)
>
> Limit[Erf[1\/Sqrt[\[Alpha]\ t]], t -> \[Infinity],
>     Assumptions -> {\[Alpha] == 1}]
>
> gives zero
>
> Any suggestions? Is this a bug?
> Bye
> Ben



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