Bicomplex Holomorphic Functions The Algebra, Geometry and Analysis of Bicomplex Numbers /

• Main Authors: Luna-Elizarrarás, M. Elena (Author), Shapiro, Michael (Author), Struppa, Daniele C. (Author), Vajiac, Adrian (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Functions of complex variables.; Mathematical physics.; Functions of a Complex Variable.; Several Complex Variables and Analytic Spaces.; Mathematical Applications in the Physical Sciences.

The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensi...

Table of Contents:

• Introduction
• 1.The Bicomplex Numbers
• 2.Algebraic Structures of the Set of Bicomplex Numbers
• 3.Geometry and Trigonometric Representations of Bicomplex
• 4.Lines and curves in BC
• 5.Limits and Continuity
• 6.Elementary Bicomplex Functions
• 7.Bicomplex Derivability and Differentiability
• 8.Some properties of bicomplex holomorphic functions
• 9.Second order complex and hyperbolic differential operators
• 10.Sequences and series of bicomplex functions
• 11.Integral formulas and theorems
• Bibliography.