Re: Problem with evaluation of Besel Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg56008] Re: [mg55963] Problem with evaluation of Besel Functions
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 13 Apr 2005 01:10:48 -0400 (EDT)
• References: <200504120926.FAA27616@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ariel sumeruk wrote:
> 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

Using approximate arithmetic near singularities can have such
consequences. This follows from the fact that the limiting value for a
multivariate function is path dependent; small perturbations might make
a denominator vanish while a numerator is "small" but not manifestly
zero. That's pretty much what happens in this example.

If you use xx->3/2 you will (appropriately) obtain Indeterminate due to
a 0/0 situation. Even this is not always going to work as you might
like, because in general numerator or denominator might be a "disguised"
zero while the other one is explicit, causing a result of zero or infinity.

Daniel Lichtblau
Wolfram Research

```

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