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Jacobi Elliptic Cliffordian Functions | | Guy Laville
; Ivan Ramadanoff
; | | Date: |
3 Feb 2005 | | Subject: | Complex Variables MSC-class: 30G35, 33E05 | math.CV | | Affiliation: | LMNO), Ivan Ramadanoff (LMNO | | 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. | | Source: | arXiv, math.CV/0502073 | | Services: | Forum | Review | PDF | Favorites | |
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