TY - JOUR
T1 - Singularities of bicomplex holomorphic functions
AU - Luna-Elizarrarás, M. Elena
AU - Perez-Regalado, C. Octavio
AU - Shapiro, Michael
N1 - Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.
PY - 2021
Y1 - 2021
N2 - In the theory of bicomplex holomorphic functions, there is not concept of isolated singularities; that is, such functions do not have singularities just at a point like holomorphic functions in one complex variable. However, there are other type of singularities that behave similarly to the isolated singularities in one complex variable. In this work, we describe how they can be classified in such a way that it resembles the classification made for the complex analysis case. It turns out that to singularities there corresponds their orders which are hyperbolic numbers with integer components, not real integers. We give also the Residue Theorem in the bicomplex analysis setting.
AB - In the theory of bicomplex holomorphic functions, there is not concept of isolated singularities; that is, such functions do not have singularities just at a point like holomorphic functions in one complex variable. However, there are other type of singularities that behave similarly to the isolated singularities in one complex variable. In this work, we describe how they can be classified in such a way that it resembles the classification made for the complex analysis case. It turns out that to singularities there corresponds their orders which are hyperbolic numbers with integer components, not real integers. We give also the Residue Theorem in the bicomplex analysis setting.
KW - bicomplex numbers
KW - hyperbolic curves
KW - singularities of bicomplex functions
UR - http://www.scopus.com/inward/record.url?scp=85106404197&partnerID=8YFLogxK
U2 - 10.1002/mma.7522
DO - 10.1002/mma.7522
M3 - Artículo
AN - SCOPUS:85106404197
SN - 0170-4214
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
ER -