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st: RE: RE: Bessel


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Bessel
Date   Mon, 3 Oct 2005 09:44:04 +0100

Recall that in Stata pi = 3.14159... is accessible to machine precision 
as either _pi or c(pi). So there is no harm done, 
and possibly some small harm avoided, in using those
inbuilt constants directly. 

Nick 
n.j.cox@durham.ac.uk 

Jhilbe@aol.com
 
> I found an  approximation to the Bessel Type 2 in an old 
> journal article. 
> Since it is an  approximation anyhow, I further simplified it 
> by calculating pi/2 
> and pi/4 to  their numeric values (to 4 decimal points), 
> which are 1.5708 and 
> 0.7854  respectively. The actual approximation I found was given as:
> J_n(x) ~  sqrt(2/(pi*x)) * sin(x-(2*n+1)*(pi/4). 
> 

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