RE: [Maxima] RE: [Maxima] Re: [Maxima-lang-fr] calcul des zeros de bessel sphérique et de sa dérivée...

There are programs specifically to find zeros of bessel functions,
e.g. mjyz0.for at http://jin.ece.uiuc.edu/routines  
I don't know if this is particularly good but..

There may be a problem in doing the obvious thing, since the evaluation of
bessel functions near a zero of a bessel function may be relatively
inaccurate.
There have been papers published in the last few years on Bessel function
evaluation, if it matters to get the answers right and fast.
RJF

> -----Original Message-----
> From: maxima-admin at math.utexas.edu 
> [mailto:maxima-admin at math.utexas.edu] On Behalf Of 
> Billinghurst, David (CALCRTS)
> Sent: Wednesday, August 09, 2006 3:43 PM
> To: Maxima
> Cc: fred
> Subject: RE: [Maxima] Re: [Maxima-lang-fr] calcul 
> des zeros de bessel sph?rique et de sa d?riv?e...
> 
> > I'm forwarding the message below which appeared on the 
> French Maxima 
> > mailing list.
> > 
> > Fred asks how to calculate the zeros of the spherical 
> Bessel function 
> > of order n and its derivative, or to be exact, (r Jn(r))' .
> 
> I am fairly sure that there is no analytic solution. 
> 
> 
> > I guess it's possible to approximate the zeros numerically 
> but surely 
> > there is a formula somewhere. Maybe Abramowitz & Stegun is 
> a place to 
> > look.
> 
> The are asymptotic approximations of Bessel functions in 
> terms of sin and cos.  These get you close to the zeros and 
> Newton-Raphson iteration will converge very nicely from there.
> 
> Have a look at A&S sections 9.2 and 9.5
> (there is an online copy at http://www.convertit.com/ )
> 
> 
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