Re: Problem with evaluation of Besel Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg55993] Re: Problem with evaluation of Besel Functions
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Wed, 13 Apr 2005 01:10:21 -0400 (EDT)
• References: <d3g8kd\$smh\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ariel sumeruk <ariel.sumeruk at gmail.com> wrote:
> I am having a problem evaluating various functions, One example is the
> following
>
> BesselJ[1.5, 0] evaluates to 0

Actually, it evaluates to 0., which is an approximate number.

By contrast, BesselJ[3/2, 0] evaluates to 0 precisely.

> but
> (BesselJ[xx, yyy] /. xx -> 1.5) /. yyy -> 0 evaluates to complex infinity

True, and that looks bad. More instructive, however, is to note that

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

evaluates to Indeterminate. Unlike ComplexInfinity, Indeterminate does not
conflict with the evaluation of BesselJ[3/2, 0]. To get a numerical answer,
rather than Indeterminate, we need to take a limit:

In[9]:= Limit[BesselJ[xx, yyy] /. xx -> 3/2, yyy -> 0]

Out[9]= 0

David Cantrell

> 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.

```

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