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Archive-Name: sci-math-faq/Quaternions
Last-modified: December 8, 1994
Version: 6.2
THEORY OF QUATERNIONIC ANALYTIC FUNCTIONS
Four-dimensional analog to the theory of complex analytic functions.
It was developed in the 1930s by the mathematician Fueter. It is based
on a generalization of the Cauchy-Riemann equations, since the
possible alternatives of power series expansions or quaternion
differentiability do not produce useful theories. A number of useful
integral theorems follow from the theory. Sudbery provides an
excellent review. Deavours covers some of the same material less
thoroughly. Brackx discusses a further generalization to arbitrary
Clifford algebras.
References
Anthony Sudbery. Quaternionic Analysis. Proc. Camb. Phil. Soc., vol.
85, pp 199-225, 1979.
Cipher A. Deavours. The Quaternion Calculus. Am. Math. Monthly, vol.
80, pp 995-1008, 1973.
Clifford analysis. F. Brackx and R. Delanghe and F. Sommen. Pitman,
1983.
_________________________________________________________________
alopez-o@barrow.uwaterloo.ca
Tue Apr 04 17:26:57 EDT 1995
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