Generalization of Weierstrassian elliptic functions to R(n)

The Weierstrassian rho, zeta and sigma functions are generalized to R(n). The n = 3 and n = 4 cases have already been used in instanton solutions which may be interpreted as explicit realizations of spacetime foam and the monopole condensate, respectively. The new functions satisfy higher dimensional versions of the periodicity properties and Legendre's relations obeyed by their familiar complex counterparts. For n = 4, the construction reproduces functions found earlier by Fueter using quaternionic methods. Integrating over lattice points along all directions but two, one recovers the original Weierstrassian elliptic functions.