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- From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz)
- Subject: sci.math FAQ: Quaternions
- Summary: Part 29 of many, New version,
- Originator: alopez-o@neumann.uwaterloo.ca
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- Date: Fri, 17 Nov 1995 17:16:05 GMT
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- Archive-Name: sci-math-faq/Quaternions
- Last-modified: December 8, 1994
- Version: 6.2
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- THEORY OF QUATERNIONIC ANALYTIC FUNCTIONS
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- 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.
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- References
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- Anthony Sudbery. Quaternionic Analysis. Proc. Camb. Phil. Soc., vol.
- 85, pp 199-225, 1979.
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- Cipher A. Deavours. The Quaternion Calculus. Am. Math. Monthly, vol.
- 80, pp 995-1008, 1973.
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- Clifford analysis. F. Brackx and R. Delanghe and F. Sommen. Pitman,
- 1983.
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- _________________________________________________________________
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- alopez-o@barrow.uwaterloo.ca
- Tue Apr 04 17:26:57 EDT 1995
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