Looking for TVM formulas

[Manolo Sobrino]

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 +...


It works nicely:

http://www.wolframalpha.com/share/clip?f...adhpbqopam

(edit n: for the general results better paste this:
z/(1 - z/(2 + z/(3 - z/(2 + z/(5 - z/(2 + z/(7 - z/(2 ))))))))-(e^z-1)
in Wolfram Alpha, the link might work, but WA/the forum seems to mess with parentheses, system/keyboard language settings and url addresses, that or I'm thick today)

(edit n+k: apparently the caret ^ isn't a proper html character and should be avoided when quoting urls, so it's better to use exp(), or ** instead)

A TI 86 is fine to evaluate this easily, because you don't have to close parentheses with it. At that order I get at least 11 digits right for |z|<1. It shouldn't be hard to code.