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.






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    alopez-o@barrow.uwaterloo.ca
    Tue Apr 04 17:26:57 EDT 1995

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