Newsgroups: sci.math,sci.answers,news.answers Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!spool.mu.edu!torn!watserv3.uwaterloo.ca!undergrad.math.uwaterloo.ca!neumann.uwaterloo.ca!alopez-o 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 Message-ID: Sender: news@undergrad.math.uwaterloo.ca (news spool owner) Approved: news-answers-request@MIT.Edu Date: Fri, 17 Nov 1995 17:16:05 GMT Expires: Fri, 8 Dec 1995 09:55:55 GMT Reply-To: alopez-o@neumann.uwaterloo.ca Nntp-Posting-Host: neumann.uwaterloo.ca Organization: University of Waterloo Followup-To: sci.math Lines: 52 Xref: senator-bedfellow.mit.edu sci.math:124403 sci.answers:3437 news.answers:57838 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