Jacobi Elliptic Cliffordian Functions
复变函数
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0502073,
title = {Jacobi Elliptic Cliffordian Functions},
author = {Guy Laville and Ivan Ramadanoff},
journal= {arXiv preprint arXiv:math/0502073},
year = {2007}
}