ABSTRACT
This chapter begins the study of holomorphic functions of a bicomplex variable. These functions have many striking similarities to holomorphic functions of a complex variable; for example, holomorphic functions of both complex and bicomplex variables can be defined either as functions which can be represented locally by power series or as functions which have a derivative. The power series definition seems to provide the easier introduction to the theory of holomorphic functions of a bicomplex variable; accordingly, this chapter is devoted to a study of infinite series, and especially to a study of functions defined by power series in ℂ2.
