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Jacobi Elliptic Cliffordian Functions

Guy Laville·Ivan Ramadanoff
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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 x^n, their derivatives, their sums, their limits (cf : z^n for classical holomorphic functions). In that context it is possible to define the same type of functions as Jacobi's.

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Guy Laville, Ivan Ramadanoff. 2005-02-03. Jacobi Elliptic Cliffordian Functions. https://arxiv.org/abs/math/0502073

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