A V Meremianin 2006 J. Phys. A: Math. Gen. 39 3099 doi:10.1088/0305-4470/39/12/017
Multipole expansions in four-dimensional hyperspherical harmonics
A V Meremianin
Show affiliationsThe technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function 
with r = r1 + r2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors 
and 
. The multipole decomposition of the function (r1 
r2)n is also derived. The proposed method can be easily generalized to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch–Gordan coefficients with particular values of parameters are presented in the closed form.
- PACS
- MSC
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15A69 Multilinear algebra, tensor products
15A03 Vector spaces, linear dependence, rank
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
- Subjects
- Dates
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Issue 12 (24 March 2006)
Received 24 October 2005, in final form 2 February 2006
Published 8 March 2006
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Multipole expansions in four-dimensional hyperspherical harmonics
A V Meremianin 2006 J. Phys. A: Math. Gen. 39 3099
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