Post Reply 
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
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
Find all posts by this user
Quote this message in a reply
Post Reply 


Messages In This Thread
Looking for TVM formulas - Dave Britten - 03-31-2014, 11:21 PM
RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 10:40 AM
RE: Looking for TVM formulas - Jeff_Kearns - 04-01-2014, 07:37 PM
RE: Looking for TVM formulas - Dieter - 04-02-2014, 12:21 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 - Dieter - 04-02-2014, 07:40 PM
RE: Looking for TVM formulas - Dieter - 04-03-2014, 01:22 PM
RE: Looking for TVM formulas - Jeff_Kearns - 04-04-2014, 09:44 PM
RE: Looking for TVM formulas - Dieter - 04-05-2014, 09:58 PM



User(s) browsing this thread: 2 Guest(s)