RE: [Maxima] Re: [Maxima-lang-fr] calcul des zeros de bessel sphérique et de sa dérivée...
Subject: RE: [Maxima] Re: [Maxima-lang-fr] calcul des zeros de bessel sphérique et de sa dérivée...
From: Billinghurst, David CALCRTS
Date: Thu, 10 Aug 2006 08:43:07 +1000
> 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/ )
NOTICE
This e-mail and any attachments are private and confidential and may contain privileged information. If you are not an authorised recipient, the copying or distribution of this e-mail and any attachments is prohibited and you must not read, print or act in reliance on this e-mail or attachments.
This notice should not be removed.