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It is well known that there is an integral theorem for quaternion-valuedfunctions analogous to Cauchys Theorem for complex-valued functions, namelyFueters Theorem. The class of quaternionic functions for which this applies aregenerally referred to as regular functions, and these provide the mostproductive means of generalising the class of holomorphic complex functions.This paper derives a second integral theorem, also analogous to CauchysTheorem, and which is believed to be quite distinct from that of Fueter,despite appearances. The paper takes the opportunity to present the basis ofthe derivation of both theorems, and also their extension to the associatedclasses of right-regular and conjugate regular functions. Both theorems canalso be extended into the biquaternionic domain in which the four quaternioncoordinates may be complex valued. This is of interest in physics as theHermitian biquaternions have a natural norm which is Minkowskian and provide anelegant formalism for Lorentz transformations.

Cauchy-like Integral Theorems for Quaternion and Biquaternion Functions