Looking for TVM formulas
04-09-2014, 01:36 PM (This post was last modified: 04-09-2014 02:15 PM by Dieter.)
Post: #27
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Looking for TVM formulas
(04-06-2014 07:46 PM)Dieter Wrote:  Since we're at it: hyperbolics can also be used for ln1+x.

$$ln(1+x) = 2 \cdot artanh(\frac{x}{x+2})$$

Seems to work well if x is not too large so that the artanh-argument does not get too close to 1.

This one seems even better and does not have problems with very large x:

$$ln(1+x) = arsinh(\frac{x^2+2x}{2+2x})$$

For better numeric accuracy this can be written as

$$y = \frac{x}{2}; z = y + \frac{y}{2y+1}$$

$$ln(1+x) = arsinh z$$

With $$z \rightarrow \infty, arsinh z \rightarrow ln 2z$$  and  $$z \rightarrow \frac{x+1}{2}$$,  so that $$arsinh z \rightarrow ln(1+x)$$.

Dieter
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 Messages In This Thread Looking for TVM formulas - Dave Britten - 03-31-2014, 11:21 PM RE: Looking for TVM formulas - Thomas Klemm - 04-01-2014, 12:17 AM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 12:43 AM RE: Looking for TVM formulas - Thomas Klemm - 04-01-2014, 04:25 AM RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 10:40 AM RE: Looking for TVM formulas - Manolo Sobrino - 04-01-2014, 09:36 AM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 01:16 PM RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 07:37 PM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 08:01 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 12:21 PM RE: Looking for TVM formulas - Dave Britten - 04-02-2014, 02:15 PM RE: Looking for TVM formulas - Thomas Klemm - 04-02-2014, 05:18 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 07:23 PM RE: Looking for TVM formulas - Dieter - 04-06-2014, 07:46 PM RE: Looking for TVM formulas - Dieter - 04-09-2014 01:36 PM RE: Looking for TVM formulas - Dave Britten - 04-01-2014, 06:01 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-02-2014, 04:55 PM RE: Looking for TVM formulas - Dieter - 04-02-2014, 07:40 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-03-2014, 01:10 AM RE: Looking for TVM formulas - Dieter - 04-03-2014, 01:22 PM RE: Looking for TVM formulas - Manolo Sobrino - 04-04-2014, 07:49 AM RE: Looking for TVM formulas - Dave Britten - 04-04-2014, 02:07 PM RE: Looking for TVM formulas - Thomas Klemm - 04-04-2014, 05:23 PM RE: Looking for TVM formulas - Jeff_Kearns - 04-04-2014, 09:44 PM RE: Looking for TVM formulas - Dave Britten - 04-04-2014, 10:12 PM RE: Looking for TVM formulas - Dieter - 04-05-2014, 09:58 PM RE: Looking for TVM formulas - Dave Britten - 04-05-2014, 11:38 PM

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