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Hostler [J. Math. Phys. 11, 2966 (1970)] has shown that Coulomb Green’s functions of different dimensionality N are related by G(N+2)=OG(N), where O is a first‐order derivative operator in the variables x and y. Thus all the even‐dimensional functions are connected, as are analogously the odd‐dimensional functions. It is shown that the operations of functional differentiation and integration can further connect the even‐ to the odd‐dimensional functions, so that Hostler’s relation can be extended to give G(N+1)=O1/2G(N)

Generalized relations among N-dimensional Coulomb Green’s functions using fractional derivatives