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Re: general formula for differentiating a spherical bessel function of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122056] Re: general formula for differentiating a spherical bessel function of
  • From: Peter Pein <petsie at dordos.net>
  • Date: Tue, 11 Oct 2011 04:23:33 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Am 09.10.2011 09:58, schrieb raj kumar:
> hi there!,
> i am trying to obtain a general formula for differentiating a
> spherical bessel function of the form SphericalBesselJ[L, kr] m times
> with respect to k
> 
> D[SphericalBesselJ[L, k Subscript[r, 2]], {k, 1}] //
>   FullSimplify // Apart=
>  (L SphericalBesselJ[L, k Subscript[r, 2]])/k -
>  SphericalBesselJ[1 + L, k Subscript[r, 2]] Subscript[r, 2]
> 
> D[SphericalBesselJ[L, k Subscript[r, 2]], {k, 2}] //
>   FullSimplify // Apart =
> ((-1 + L) L SphericalBesselJ[L, k Subscript[r, 2]])/k^2 + (
>  2 SphericalBesselJ[1 + L, k Subscript[r, 2]] Subscript[r, 2])/k -
>  SphericalBesselJ[L, k Subscript[r, 2]] \!
> \*SubsuperscriptBox[\(r\), \(2\), \(2\)]
> and so on.
> is there a general formula in terms of SphericalBesselJ[L, kr]?
> 

as far as I understand, the third formula on this page might be of
(minor?) help:
http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/20/02/02/




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