request help

• To: mathgroup at smc.vnet.net
• Subject: [mg116189] request help
• From: Berihu Teklu <berihut at gmail.com>
• Date: Fri, 4 Feb 2011 01:41:22 -0500 (EST)

```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]

```

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