Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110389] Re: Simplification question
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 16 Jun 2010 05:39:00 -0400 (EDT)

On 15 Jun 2010, at 15:30, Yaroslav Bulatov wrote:

> I'd like to verify that the following expression is true for a,b real.
> It seems to hold numerically.
>
> 1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] ====
> ArcTanh[Tanh[a] Tanh[b]]
>
> I tried Reduce and combinations of TrigToExp/Simplify with no luck,
> any suggestions?
>
Fix b and note that you get an analytic function of one variable a. Now note that

D[(1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] -
    ArcTanh[Tanh[a] Tanh[b]]), a] // Simplify

0

and


1/2 ( Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] -
    ArcTanh[Tanh[a] Tanh[b]]) /. a->0

 0

Since the function is analytic, this is enough to prove that the expression is identically zero.


  • Prev by Date: Re: How to construct symmetric matrix from just a one half matrix
  • Next by Date: Re: DiscretePlot
  • Previous by thread: Re: Simplification question
  • Next by thread: Re: Simplification question