Re: Any simpler form for f(x) = exp(-a/x) - exp(-b/x)?
- From: Martin Brown <|||newspam|||@nezumi.demon.co.uk>
- Date: Fri, 24 Aug 2007 09:36:38 -0700
On Aug 24, 3:09 am, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
spasmous <spasm...@xxxxxxxxx> writes:
I have the expression above and am wondering if it simplifies any
further. I've messed around with cosh and sinh but it gets ugly quick.
Just wondering if someone knows of any tricks.
Depends on what you consider simpler. How about
2 exp(-(a+b)/(2 x)) sinh((b-a)/(2 x)) ?
Numerically there might be some advantage in computing it as
exp(-ax/x) ( 1 - exp(-(b-a)/x )
As there is often direct hardware support for computing (exp(x) - 1)
accurately.
Regards,
Martin Brown
.
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