See reader questions & answers on this topic!  Help others by sharing your knowledge ArchiveName: scimathfaq/Quaternions Lastmodified: December 8, 1994 Version: 6.2 THEORY OF QUATERNIONIC ANALYTIC FUNCTIONS Fourdimensional 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 CauchyRiemann 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 199225, 1979. Cipher A. Deavours. The Quaternion Calculus. Am. Math. Monthly, vol. 80, pp 9951008, 1973. Clifford analysis. F. Brackx and R. Delanghe and F. Sommen. Pitman, 1983. _________________________________________________________________ alopezo@barrow.uwaterloo.ca Tue Apr 04 17:26:57 EDT 1995 User Contributions:
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