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It is shown that the f-dimensional nonrelativistic Coulomb Green's function and the associated reduced Green's functions can be obtained by differentiation of the corresponding functions in the 1-dimensional (f odd) or 2-dimensional (f even) case. A new expansion of the 3-dimensional coordinate-space Coulomb Green's function and a new sum formula for a product of two Laguerre polynomials with different arguments are derived.
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Levere Hostler (1970) studied this question.
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