Odd little Bessel function quirk
- To: mathgroup at smc.vnet.net
- Subject: [mg79035] Odd little Bessel function quirk
- From: AES <siegman at stanford.edu>
- Date: Mon, 16 Jul 2007 02:19:50 -0400 (EDT)
- Organization: Stanford University
[Indented lines are Output cells; others are Input cells]
f[r_] := If[r ¾ 1, BesselJ[0, \ r], BesselK[0, r]]
f[r]
If[r ¾ 1, BesselJ[0, r], BesselK[0, r]]
D[f[r], r]
If[r ¾ 1, 1/2 (BesselJ[-1, r] - BesselJ[1, r]),
1/2 (-BesselK[-1, r] - BesselK[1, r])]
D[f[r], r] /. r ¾ 1 -> True
-BesselJ[1, r]
D[f[r], r] /. r ¾ 1 -> False
-BesselK[1, r]
Nothing erroneous here (so far as I know) -- but how come the results of
the (superfluous) 4th and 5th Input lines are simplified, but the 3rd
one is not? [When I'm struggling with Bessel functions, I can use all
the simplification I can get!]