Epilogue

This book has presented an introduction to the theory of functions of a bicomplex, and of a multicomplex, variable. This theory combines important parts of the theory of functions of a real variable and also of a complex variable to construct a theory of a new class of functions known as holomorphic functions of a (bicomplex or) multicomplex variable. This theory seems to be an altogether natural continuation of the theory of functions of a complex variable. The theory of functions of a complex variable gains much relative simplicity from the fact that it is a two-dimensional theory; the theory of functions in ℂ _n gains much interest and difficulty from the fact that it is a 2 ⁿ -dimensional theory. But C_n has a structure which provides some special tools which facilitate the study of certain high-dimensional spaces where geometric intuition is largely wanting.