Quaternionic analysis

Summary

Quaternionic analysis studies functions of a quaternion variable with quaternion values, by analogy with complex analysis. The naive analogue of the complex derivative is too restrictive. So the central class is that of Fueter regular functions, the solutions of a quaternionic Cauchy–Riemann equation. These functions have an integral formula like Cauchy's and are harmonic in $\R^4$. A wider theory, Clifford analysis, extends these ideas to all dimensions.