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Re: request help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116207] Re: request help
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sat, 5 Feb 2011 05:44:49 -0500 (EST)

You'd have call Solve this way:

Solve[Dis[r, n] == z, r]

but Mathematica (of course) cannot solve it. I doubt that god could.

You might try an approximation such as

series = Normal@Series[Dis[r, n], {r, 0, 5}];
Solve[series == z, r]

but that may not be useful to you.

Otherwise, you'll have to give n and z numeric values and use NSolve or  
FindRoot.

Bobby

On Fri, 04 Feb 2011 00:41:22 -0600, Berihu Teklu <berihut at gmail.com> wrote:

> I need to invert a real function of two real variables Dis[r, n] with
> respect to the first variable r, while the second variable n is fixed.
> The function is rather difficult, that I couldn't invert it. this is
> kindly request you to write me any comments on the attached notebook.
>
> Many thanks for any help,
>
> Berihu
>
>
> Dis[r_, n_] :=
>  1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] -
>     2 (2 + Sqrt[(1 + 2 n)^2]) Log[
>       2 + Sqrt[(1 + 2 n)^2]] - (-2 +
>        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 +
>        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 +
>        Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[
>       2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 +
>        Sqrt[((1 + 2 n)^2 (1 + 2 n -
>           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[-2 +
>        Sqrt[((1 + 2 n)^2 (1 + 2 n -
>           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] + (2 +
>        Sqrt[((1 + 2 n)^2 (1 + 2 n -
>           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[
>       2 + Sqrt[((1 + 2 n)^2 (1 + 2 n -
>           2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]])
>
> Solve[1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] -
>      2 (2 + Sqrt[(1 + 2 n)^2]) Log[
>        2 + Sqrt[(1 + 2 n)^2]] - (-2 +
>         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 +
>         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 +
>         Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[
>        2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 +
>         Sqrt[((1 + 2 n)^2 (1 + 2 n -
>            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[-2 +
>         Sqrt[((1 + 2 n)^2 (1 + 2 n -
>            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] + (2 +
>         Sqrt[((1 + 2 n)^2 (1 + 2 n -
>            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[
>        2 + Sqrt[((1 + 2 n)^2 (1 + 2 n -
>            2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]]) ==
>   Dis[r, n], r]
>


-- 
DrMajorBob at yahoo.com


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