Re: Odd little Bessel function quirk
- To: mathgroup at smc.vnet.net
- Subject: [mg79069] Re: [mg79035] Odd little Bessel function quirk
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Tue, 17 Jul 2007 03:29:13 -0400 (EDT)
- Reply-to: hanlonr at cox.net
In general, simplification is not done until you ask for it.
f[r_] := If[r < 1, BesselJ[0, r], BesselK[0, r]];
D[f[r], r] // Simplify
Piecewise[{{-BesselJ[1, r], r < 1}}, -BesselK[1, r]]
Bob Hanlon
---- AES <siegman at stanford.edu> wrote:
> [Indented lines are Output cells; others are Input cells]
>
>
> f[r_] := If[r =C2=BE 1, BesselJ[0, \ r], BesselK[0, r]]
>
> f[r]
>
> If[r =C2=BE 1, BesselJ[0, r], BesselK[0, r]]
>
> D[f[r], r]
>
> If[r =C2=BE 1, 1/2 (BesselJ[-1, r] - BesselJ[1, r]),
> 1/2 (-BesselK[-1, r] - BesselK[1, r])]
>
> D[f[r], r] /. r =C2=BE 1 -> True
>
> -BesselJ[1, r]
>
> D[f[r], r] /. r =C2=BE 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!]
>