general formula for differentiating a spherical bessel function of
- To: mathgroup at smc.vnet.net
- Subject: [mg122021] general formula for differentiating a spherical bessel function of
- From: raj kumar <rajesh7796gm at gmail.com>
- Date: Sun, 9 Oct 2011 03:52:56 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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]?