| Abstract: | The well-known Jacobi elliptic functions sn(z), cn(z), dn(z) are defined in higher dimensional spaces by the following method. Consider the Clifford algebra of the antieuclidean vector space of dimension 2m + 1. Let x be the identity mapping on the space of scalars + vectors. The holomorphic Cliffordian functions may be viewed roughly as generated by the powers of x, namely xn , their derivatives, their sums, their limits (cf: zn for classical holomorphic functions). In that context it is possible to define the same type of functions as Jacobi's. |
