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]?