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 Post subject: approximation of Ln within TanPosted: Mon, 2 Mar 2009 10:21:22 UTC
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Joined: Sat, 15 Dec 2007 15:57:40 UTC
Posts: 67
Location: Kyoto
I have a very complicated function where my variable x lies within a Ln that lies within a Tan.
I would very much like to have a function that could approximate it so I can estimate values of x.
I have no idea how to do it. does somebody have an idea?

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 Post subject: Posted: Mon, 2 Mar 2009 21:06:44 UTC
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Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
It really depends on the details of the function, and the range of values of x.

We could use

so (for example)

but this works only over the range 1/2 < x < 5/2

If the function is complex, you might be able to use

Are you looking for a polynomial?

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 Post subject: Posted: Thu, 5 Mar 2009 09:29:51 UTC
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Joined: Sat, 15 Dec 2007 15:57:40 UTC
Posts: 67
Location: Kyoto
It's not that I especifically need a polynomial, I don't have anything .
The hardest thing is indeed the Ln(x), I do not know how to work that there. I have only seen approximations for Ln(x+1) or very bad approximations for Ln(x)..

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 Post subject: Posted: Thu, 5 Mar 2009 16:52:37 UTC
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Joined: Tue, 20 Nov 2007 04:36:12 UTC
Posts: 826
Location: Las Cruces
The western novelist Louis L'Amour observed that beginning writers often waste pages and pages writing about their story instead of telling their story. Unless the game here to guess what function you are talking about, you could simply write it down. Also, in this age of computers, why do you need an approximation?

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 Post subject: Posted: Mon, 9 Mar 2009 11:44:13 UTC
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Joined: Sat, 15 Dec 2007 15:57:40 UTC
Posts: 67
Location: Kyoto
Well, this is the reason....

I'm looking for the x...

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 Post subject: Posted: Tue, 10 Mar 2009 03:01:17 UTC
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Joined: Tue, 20 Nov 2007 04:36:12 UTC
Posts: 826
Location: Las Cruces
But it still isn't clear whether you need a numerical method (one like "bisection" that can be implemented as a computer program) to find x or whether you need symbolic expression for x.

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 Post subject: Posted: Wed, 18 Mar 2009 10:58:25 UTC
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Joined: Sat, 15 Dec 2007 15:57:40 UTC
Posts: 67
Location: Kyoto
I would like a symbolic expression for x...

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