Quaternions were introduced in 1843 by the Irish mathematician William Rowan Hamilton. Quaternion analysis or more generally, hypercomplex analysis - the most natural and close generalization of complex analysis to higher dimensions - is nowadays recognized as a powerful tool for modeling and solving problems in both theoretical and applied mathematics.
QuaternionAnalysis is a Mathematica add-on application for manipulating quaternion valued functions, regular (or monogenic) in the sense of Rudolf Fueter. It is closely based on the book Holomorphic functions in the plane and n-dimensional space, by K. Guerlebeck, K. Habetha and W. Sproessig.
QuaternionAnalysis package adds functionalities to the Quaternions package for implementing Hamilton's quaternion algebra and provides tools for manipulating regular quaternion valued functions. Some of the added new features include the possibility of performing operations on functions defined in $\mathbb{R}^{n+1}$, $n\geq2$.