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

**References**:**Problem with evaluation of Besel Functions***From:*Ariel sumeruk <ariel.sumeruk@gmail.com>