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Re: Problem with evaluation of Besel Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg56010] Re: Problem with evaluation of Besel Functions
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Wed, 13 Apr 2005 01:10:52 -0400 (EDT)
• References: <d3g8kd$smh$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

This does what you want:

Limit[(BesselJ[xx, yyy] /. xx -> 3/2) , yyy -> 0 ]

1. Use rational fractions rather than reals to keep the calculations exact. 
This gives the following result for (BesselJ[xx, yyy] /. xx -> 3/2):

(Sqrt[2/Pi]*(-Cos[yyy] + Sin[yyy]/yyy))/Sqrt[yyy]

2. Use Limit[(...), yyy -> 0 ] rather than (...)/.yyy -> 0 to correctly 
handle the behaviour near yyy=0.

Steve Luttrell

"Ariel sumeruk" <ariel.sumeruk at gmail.com> wrote in message 
news:d3g8kd$smh$1 at smc.vnet.net...
> Hello
> I am having a problem evaluating various functions, One example is the 
> following
>
> BesselJ[1.5, 0] evaluates to 0 but
> (BesselJ[xx, yyy] /. xx -> 1.5) /. yyy -> 0 evaluates to complex infinity
>
> I seem to encounter many of these problems with Bessel and Legendre
> functions where I get actual diffrent numerical results depending on
> How I set the parameters.
> Thanks for anyone who might help
> Ariel
>