Looking for TVM formulas

[Manolo Sobrino]

(04-02-2014 07:40 PM)Dieter Wrote:  

(04-02-2014 04:55 PM)Manolo Sobrino Wrote:  I'd try continued fractions (check Abramowitz: (4.2.40)). I like this one:
e^z - 1= z/(1 - z/(2 + z/(3 - z/(2 + z/(5 - z/(2 + z/(7 - z/(2 +...
...
At that order I get at least 11 digits right for |z|<1. It shouldn't be hard to code.

ln 0,9 < z < ln 2 is all that's required. ;-)
With terms up to n = 9 the result has 11 valid digits.

Dieter

You're right, lower bound is wrong for 11 digits. Yet I get 11 up to -0.38. Where did you get the analytical expression for the bounds? (yeah, I'm asking for "here be dragons" stuff )