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Re: Problem with evaluation of Besel Functions

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

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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