Bessel Function Bug
- To: mathgroup at smc.vnet.net
- Subject: [mg9899] Bessel Function Bug
- From: Peter <psalzman at landau.ucdavis.edu>
- Date: Sun, 30 Nov 1997 20:16:46 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Hello Mathgroup,
I am having a hard time figuring this out--perhaps it's a bug or perhaps
not.
According to Jackson pg 740 eq 16.9
pi Sin[x]
j[0,x] = Sqrt[--] BesselJ[.5, x] = ------
2x x
where j[0,x] is the spherical bessel function of order zero.
However, when I plot:
pi Sin[x]
Sqrt[--] BesselJ[.5, x] and ------
2x x
Mathematica says the first function is odd about the origin and the
Sin[x]/x is even about the origin. Modulo the minus sign difference on
the negative axis, they are the same.
Either Jackson neglected to say that there is a different choice of
branch for the square root when x<0 or Mathematica is giving the wrong
sign for the Bessel function of half order when x<0.
Offhand, does anyone know which explanation is correct?
If you look at Jackson's expression on page 104 for the Bessel functions
(3.82) it seems to suggest that Mathematica is wrong, although again,
perhaps there's a choice of branch that he's not explicitly saying.
Peter
ps- I'm using Mathematica 3.0.1
--
Never criticize a man till you've walked a mile in his shoes. That way,
you'll be a mile away from him and have his shoes as well.
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