It is well known that there is an integral theorem for quaternion-valued
functions analogous to Cauchys Theorem for complex-valued functions, namely
Fueters Theorem. The class of quaternionic functions for which this applies are
generally referred to as regular functions, and these provide the most
productive means of generalising the class of holomorphic complex functions.
This paper derives a second integral theorem, also analogous to Cauchys
Theorem, and which is believed to be quite distinct from that of Fueter,
despite appearances. The paper takes the opportunity to present the basis of
the derivation of both theorems, and also their extension to the associated
classes of right-regular and conjugate regular functions. Both theorems can
also be extended into the biquaternionic domain in which the four quaternion
coordinates may be complex valued. This is of interest in physics as the
Hermitian biquaternions have a natural norm which is Minkowskian and provide an
elegant formalism for Lorentz transformations.Comment: 20 pages, 1 Figur